题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043641-48117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043641-61220.png)
(1) 求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043641-97109.png)
(2) 若关于x的方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-54823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-32736.png)
(3) 证明:对任意的自然数n,有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-51730.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-74449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-80699.png)
解析
试题分析:(1)先有已知条件写出
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-59508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043641-97109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-54823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-27331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-54823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-74619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-74619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043644-82822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-27331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043644-55957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-51730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043644-48072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043644-58669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-53171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-63054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-40868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-21236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-19025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-21236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043646-89804.png)
试题解析:(1) 由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043646-66608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043646-42857.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043646-54185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-59508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043647-46466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043647-80796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-74449.png)
经检验
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-74449.png)
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-74449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043647-64620.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-54823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043647-98946.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-27331.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-54823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-74619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-74619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043648-79662.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043648-12737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043648-60166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043648-76771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043649-57561.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043649-82903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043649-28501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043648-76771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043649-32011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043644-55957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043649-63602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043650-18054.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043647-64620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043650-81519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043650-80934.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043650-82674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043650-71212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043651-63756.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043651-38631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043651-19284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89552.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043651-22425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043651-81803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043645-63054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043643-89552.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043652-72339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043652-53294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043646-54185.png)
对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043652-93040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043652-81364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043653-43098.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043653-59648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043653-24222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043653-87284.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043653-96114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043654-95019.png)
对任意的自然数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043652-93040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043642-51730.png)
核心考点
试题【已知函数若函数在x = 0处取得极值.(1) 求实数的值;(2) 若关于x的方程在区间[0,2]上恰有两个不同的实数根,求实数的取值范围;(3) 证明:对任意的】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043625-11439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043625-51940.png)
(1) 求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043625-47478.png)
(2) 若关于x的方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043625-52823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043626-82298.png)
(3)证明:对任意的正整数n,不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043626-82340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043614-50250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043614-91841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043614-54461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043614-61692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043614-63568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-15127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-57718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-32579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-56670.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-32579.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043615-32579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043603-66743.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043603-88533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043603-29383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043604-86535.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043604-27958.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043604-85594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043604-71236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043604-29107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043538-79071.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043538-81272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043538-16160.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043538-84972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043539-18497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043539-49197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043539-93102.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043539-10821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043540-78982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043540-37758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043540-91440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043525-65814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043525-19802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-26551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-85821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-72242.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-83090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-49235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-75619.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-62308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043526-65576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043527-93541.png)
(3)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043527-78537.png)
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