证明：设f(x)在x=0连续,且lim(x→0) (f(x)/x)=1,则必有f'(0)=1
人气：113 ℃ 时间：2020-06-16 07:46:20
解答
因为lim(x→0) (f(x)/x)=1 所以,x与f(x)为等价无穷小:f(x) .x趋于0时,f(x)也趋于0
所以：f(0)=0
f'(0)= lim(x→0) [f(x)-f(0)]/(x-0)
= lim(x→0) f(x)/x
= 1
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