2023河南专升本高数证明题。

2023-04-03 10:16 作者:无名过客_隔壁老贾 0人读过 | 我要投稿

4.2河南专升本得高数证明题。

思路是直接令辅助函数求最小值即可，算是看着复杂单但并不算太难，但做的慢的大题基本都没时间看了。

51.求证对于任意x和m>0都有

$%5Cln%20(x%5E2%2Bm)%2B%5Cfrac%7Bm%7D%7Bx%5E2%2Bm%7D%5Cgeq%20%5Cln%20m%20%2B%201$

参考解答：

$%E4%BB%A4F(x)%20%3D%20%5Cln%20(x%5E2%2Bm)%2B%5Cfrac%7Bm%7D%7Bx%5E2%2Bm%7D%20-%20%20%5Cln%20m%20-%201%20%5C%5C%0A%E6%98%BE%E7%84%B6F(x)%E5%9C%A8R%E4%B8%8A%E8%BF%9E%E7%BB%AD%E5%8F%AF%E5%AF%BC%2C%E4%B8%94F(0)%20%3D%200%20%5C%5C%0AF'(x)%20%3D%20%5Cfrac%7B2x%7D%7Bx%5E2%2Bm%7D-%5Cfrac%7B2xm%7D%7B(x%5E2%2Bm)%5E2%7D%3D%20%20%5Cfrac%7B2x%5E3%7D%7B(x%5E2%2Bm)%5E2%7D%20(%E9%80%9A%E5%88%86)%5C%5C%0A%E4%BB%A4F'(x)%3D0%E5%BE%97x%3D0%2C%E5%BD%93x%3E0%E6%97%B6F'(x)%3E0%3B%E5%BD%93x%3C0%E6%97%B6F'(X)%3C0%5C%5C%0A%E5%8D%B3x%3D0%E4%B8%BAF(x)%E6%9E%81%E5%B0%8F%E5%80%BC%E7%82%B9%EF%BC%8C%E6%9C%89F(x)%20%5Cgeq%20F(0)%3D0%5C%5C%0A%E5%8D%B3%5Cln%20(x%5E2%2Bm)%2B%5Cfrac%7Bm%7D%7Bx%5E2%2Bm%7D%5Cgeq%20%20%5Cln%20m%20%2B%201%20(%E7%A7%BB%E9%A1%B9)%5C%5C%0A%E5%BE%97%E8%AF%81$