1 . 已知函数
(
为常数,
).
(1)求函数
的零点个数;
(2)已知实数
、
、
为函数
的三个不同零点.
①如果
,
,求证
;
②如果
,且
、
、
成等差数列,请求出
、
、
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0c8686d4cd6fd08b0a8214b94523e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a410c1e7bf7ba96d2c1f35ef2e99af29.png)
②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2 . 设
是大于零的实数,向量
,其中
,定义向量
,记
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44633ffd37d8fee62ce3477508f356ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84602b7d09473768dc77d482199c2f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2db63581a58ca4ee8a97934845dabfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac81323746fc7c43b49ed29c7fa43a67.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2022高三·全国·专题练习
解题方法
3 . (1)已知
,比较
与
的大小,试将其推广至一般性结论并证明;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7484d9b1e33ed553e44955bf41730c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d2278151be65f6aea061e897c39975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6c44cc2b5c4dc6d062db0e45c9eb4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41029967073b4987a23e89b379f23758.png)
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