f(x)=f(0)+x+a(x),且lim (a(x)/x)=0 【x趋于0】,则f'(0)=_数学解答

f(x)=f(0)+x+a(x),且lim (a(x)/x)=0 【x趋于0】,则f'(0)=

人气：482 ℃　时间：2020-05-24 23:22:53

解答

f'(0)=lim(x->0) [f(x)-f(0)]/[x-0]
=lim(x->0) [x+a(x)]/x
=lim(x->0) 1+a(x)/x
= 1+0
=0