1 . 已知
.用数学归纳法证明
,请补全证明过程:(1)当
时,
;(2)假设
时命题成立,即
,则当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5654b1ff5304be749e5e9d2ca430251b.png)
______
,即当
时,命题成立.综上所述,对任意
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0327c94eb3f2598463855331efd863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfc470fed690793d4909a5cfe4009e3.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d853673eda54d6bc06e912b696e03b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5654b1ff5304be749e5e9d2ca430251b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94254e445240fc841982c4ad57dee344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfc470fed690793d4909a5cfe4009e3.png)
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2 . 如图是数学家Germinal Dandelin用来证明一个平面截圆锥得到的截口曲线是椭圆的模型(称为“Dandelin双球”);在圆锥内放两个大小不同的小球,使得它们分别与圆锥的侧面、截面相切,设图中球
,球
的半径分别为
和
,球心距离
,截面分别与球
,球
切于点
,
,(
,
是截口椭圆的焦点),则此椭圆的离心率等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647af54e46e22ea0160071ca6eacb1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2019/5/14/2203713737646080/2204045863878656/STEM/348be02c-ccee-4178-9cfb-64a51f00c710.png)
您最近一年使用:0次
2019-05-15更新
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3034次组卷
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11卷引用:【市级联考】安徽省合肥市2019届高三第三次教学质量检测数学理科试题
【市级联考】安徽省合肥市2019届高三第三次教学质量检测数学理科试题重庆市西南大学附属中学2020-2021学年高二上学期期中数学试题(已下线)专题9.5 椭圆 (精练)-2021年高考数学(理)一轮复习讲练测黑龙江省哈尔滨市第三中学2021-2022学年高二上学期10月月考数学试题(已下线)专题5.1 求解曲线的离心率的值或范围问题-玩转压轴题,进军满分之2021高考数学选择题填空题(已下线)第三章 圆锥曲线与方程(提分小卷)-【单元测试】2021-2022学年高二数学尖子生选拔卷(苏教版2019选择性必修第一册)江西省新余市2022届高三第二次模拟考试数学(理)试题(已下线)专题22 圆锥曲线的离心率问题-1重庆市万州第二高级中学2024届高三上学期8月月考数学试题广东省广州中学2023-2024学年高二上学期期中数学试题重庆市第七中学校2023-2024学年高二上学期第三次月考数学试题