当前位置:首页 > 高考 > 数学试卷

【334322】2022年高考天津卷回忆版数学真题

时间:2025-01-21 18:00:26 作者: 字数:13404字
简介:

…………○…………外…………○…………装…………○…………订…………○…………线…………○…………

学校:___________姓名:___________班级:___________考号:___________

…………○…………内…………○…………装…………○…………订…………○…………线…………○…………

Shape2

绝密·启用前

2022年高考天津卷(回忆版)数学真题

题号

总分

得分






注意事项:

1.答题前填写好自己的姓名、班级、考号等信息

2.请将答案正确填写在答题卡上



评卷人

得分




一、单选题

1.设全集 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,集合 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>        
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

2. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”是“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”的(       
A
.充分不必要条件
B
.必要不充分条件
C
.充要条件
D
.既不允分也不必要条件

3.函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

4. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 是双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的两个焦点,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的准线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 过双曲线的焦点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,准线与渐近线交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则双曲线的标准方程为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

5.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,关于该函数有下面四个说法:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的最小正周期为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上单调递增;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值域为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象可由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象向左平移 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个单位长度得到.
以上四个说法中,正确的个数有(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

评卷人

得分




二、填空题

6.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的大小关系为_____________.

7.化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ____________

8.如图是两个直三棱柱重叠后的图形,重叠后的底面为正方形,两个直三棱柱底面是顶角为120°,腰为3的等腰三角形,则该几何体的体积为_______________.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

9.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 是虚数单位,化简 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的结果为_______

10. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的展开式中的常数项为______.

11.若直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 被圆 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 所截得的弦长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值为_____

12.已知函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个零点,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围是______.

评卷人

得分




三、双空题

13.现有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 张扑克牌(去掉大小王);每次取一张,取后不放回,则两次都抽到A的概率为____________;在第一次抽到A的条件下,第二次抽到A的概率是____________

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 表示 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ___________,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的最大值为____________

评卷人

得分




四、解答题

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中,角ABC所对的边分别为abc.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
(1)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的大小;
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值;
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值.

16.直三棱柱 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中点.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(1)
求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
求直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的正弦值;
(3)
求平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的余弦值.

17.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 是等差数列,其前n项和为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 是等比数列, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(1)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的通项公式;
(2)
证明: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

18.已知椭圆 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的上顶点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,右顶点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,右焦点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(1)
求椭圆的离心率 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
已知直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与椭圆有唯一公共点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> (异于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ),若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,求椭圆的标准方程.

19.已知函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(1)
求曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 在点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 处的切线方程;
(2)
若曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有公共点,
i)当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围;
ii)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

参考答案

1.D

【解析】
先求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,再根据交集的定义可求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
故选:D.

2.A

【解析】
依据充分不必要条件的定义去判定“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”与“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”的逻辑关系即可.
由题意,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数,故充分性成立;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数,但 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 不为整数,故必要性不成立;
所以“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”是“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为整数”的充分不必要条件.
故选:A.

3.A

【解析】
分析函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的定义域、奇偶性及其在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上的函数值符号,结合排除法可得出合适的选项.
函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的定义域为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
则函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为奇函数,排除CD选项;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,排除B选项.
故选:A.

4.C

【解析】
由已知可得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值,求出点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的坐标,分析可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由此可得出关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的方程组,解出这三个量的值,即可得出双曲线的标准方程.
抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的准线方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
不妨设点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为第二象限内的点,联立 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
所以, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,因此,双曲线的标准方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故选:C.

5.A

【解析】
根据三角函数的图象与性质,以及变换法则即可判断各说法的真假.
因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的最小正周期为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,①不正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上递增,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上单调递增,②正确;因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,③不正确;
由于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象可由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象向右平移 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个单位长度得到,④不正确.
故选:A

6. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ## <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
利用幂函数、对数函数的单调性结合中间值法可得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的大小关系.
因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

7.2

【解析】
根据对数的性质可求代数式的值.
原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
故答案为:2.

8.27

【解析】
作出几何体直观图,由题意结合几何体体积公式即可得组合体的体积.
该几何体由直三棱柱 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 及直三棱柱 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 组成,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> M,如图,
因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
因为重叠后的底面为正方形,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,
在直棱柱 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面BHC,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
设重叠后的EG <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 交点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
则该几何体的体积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为:27.

9. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ## <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
根据复数代数形式的运算法则即可解出.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

10. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
由题意结合二项式定理可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的展开式的通项为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,代入即可得解.
由题意 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的展开式的通项为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的展开式中的常数项为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

11. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
计算出圆心到直线的距离,利用勾股定理可得出关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的等式,即可解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的圆心坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,半径为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
圆心到直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
由勾股定理可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

12. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,分析可知函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有一个零点,可得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围,然后对实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围进行分类讨论,根据题意可得出关于实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的不等式,综合可求得实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
要使得函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个零点,则函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有一个零点,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,作出函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象如下图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
此时函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 只有两个零点,不合乎题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,设函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的两个零点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
要使得函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个零点,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
所以, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,作出函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的图象如下图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
由图可知,函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的零点个数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,合乎题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,设函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的两个零点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
要使得函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 至少有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 个零点,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,此时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
综上所述,实数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的取值范围是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

13.      <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>       <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
由题意结合概率的乘法公式可得两次都抽到A的概率,再由条件概率的公式即可求得在第一次抽到A的条件下,第二次抽到A的概率.
由题意,设第一次抽到A的事件为B,第二次抽到A的事件为C,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

14.      <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>       <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
法一:根据向量的减法以及向量的数乘即可表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为基底,表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,再根据向量夹角公式以及基本不等式即可求出.
法二:以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为原点建立平面直角坐标系,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的轨迹为以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为圆心,以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为半径的圆,方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即可根据几何性质可知,当且仅当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 相切时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 最大,即求出.
方法一:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,当且仅当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时取等号,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
方法二:如图所示,建立坐标系:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的轨迹是以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为圆心,以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为半径的圆,当且仅当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 相切时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 最大,此时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

15.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
1)根据余弦定理 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 以及 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 解方程组即可求出;
2)由(1)可求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,再根据正弦定理即可解出;
3)先根据二倍角公式求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,再根据两角差的正弦公式即可求出.
1)因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,代入得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
2)由(1)可求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,又 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
3)因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,又 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> , 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

16.(1)证明见解析
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
1)以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为坐标原点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 所在直线分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 轴建立空间直角坐标系,利用空间向量法可证得结论成立;
2)利用空间向量法可求得直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的正弦值;
3)利用空间向量法可求得平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的余弦值.
1)证明:在直三棱柱 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 为坐标原点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 所在直线分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 轴建立如下图所示的空间直角坐标系, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,易知平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的一个法向量为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
2)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的法向量为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,取 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .因此,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的正弦值为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
3)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的法向量为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,取 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,因此,平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 与平面 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 夹角的余弦值为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

17.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
证明见解析
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
1)利用等差等比数列的通项公式进行基本量运算即可得解;
2)由等比数列的性质及通项与前n项和的关系结合分析法即可得证;
3)先求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,进而由并项求和可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,再结合错位相减法可得解.
1)设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 公差为d <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 公比为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 舍去),所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
2)证明:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 所以要证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 显然成立,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
3)因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,作差得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .

18.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

【解析】
1)根据已知条件可得出关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的等量关系,由此可求得该椭圆的离心率的值;
2)由(1)可知椭圆的方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,将直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的方程与椭圆方程联立,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,求出点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的坐标,利用三角形的面积公式以及已知条件可求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的值,即可得出椭圆的方程.
1)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,离心率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
2)解:由(1)可知椭圆的方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,易知直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的斜率存在,设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 的方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,联立 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,① <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,②由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,③联立①②③可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故椭圆的标准方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>

19.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>
(2)
i <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ;(ii)证明见解析

【解析】
1)求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 可求切线方程;
2)(i)当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有公共点即为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上有零点,求导后分类讨论结合零点存在定理可求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
ii)曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有公共点即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,利用点到直线的距离得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,利用导数可证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,从而可得不等式成立.
1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 在点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 处的切线方程为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .
2)(i)当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, 因为曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有公共点,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有解,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上有解,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上有零点,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 恒成立,此时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上无零点,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上恒成立,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为增函数,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上无零点,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为增函数,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上存在唯一零点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ;故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ;所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为减函数,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为增函数,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上有零点,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为增函数,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> .ii)因为曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有公共点,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 有解 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,该式不成立,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> . <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,考虑直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 表示原点与直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上的动点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 之间的距离,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,下证:对任意 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,总有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,证明:当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 成立. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时,即证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> (不恒为零),故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为减函数,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 成立.综上, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 成立.下证:当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 恒成立, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上为增函数,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 恒成立.下证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 上恒成立,即证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,而 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,故 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 成立. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/801/" title="回忆" class="c1" target="_blank">回忆</a> <a href="/tags/1180/" title="天津" class="c1" target="_blank">天津</a> 成立.


Shape4 3页,总1