设f(x)=√x,求limf(x+h)-f(x)/h (h趋向于0)_数学解答

设f(x)=√x,求limf(x+h)-f(x)/h (h趋向于0)

人气：443 ℃　时间：2020-10-02 04:48:08

解答

= lim [√(x+h) - √x /h]
= lim{ √x * [√(x+h) / √x ] -√x /h }
= lim{ √x * [√(x+h) / √x - 1/h }
= lim{ √x * [h√(x+h) - √x ] / (√x h )}
= lim [ - √x /h]
趋于负无穷大