证明不等式|arctanx-arctany|
问题描述：
证明不等式|arctanx-arctany|
答
令f(x)=arctanx
则(arctana-arctanb)/(a-b)=f'(c)=1+1/(1+c^2)a且c上式添个绝对值仍是小于1
所以|arctanx-arctany|你应该大学了吧 别告诉我还是初中
答
设f(a) = arctan(a),f'(a) = 1/(1 + a²)
f(a)在(x,y)连续可导,根据拉格朗日中值定理,
| arctanx - arctany | = 1/(1 + c²) * | x - y | 当a = b = 0时arctanx = arctany = 0
∴
| arctanx - arctany | ≤ | x - y |