lim((1/(x+h)-1/x)*1/h)h趋向于0

题目详情

lim((1/(x+h)-1/x)*1/h) h趋向于0

▼优质解答

答案和解析

lim(h->0)[(1/(x+h)-1/x)/h]=lim(h->0)[(x-(x+h))/(xh(x+h))] (分子分母同乘x(x+h))
=lim(h->0)[(-h)/(xh(x+h))]
=lim(h->0)[-1/(x(x+h))]
=-1/(x(x+0))
=--1/x^2.

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