lim(x→0)f(x)/x存在
说明x→0,lim f(x)=f(0)=0
所以
lim f(x)/x=lim [f(x)-f(0)]/x=f'(0)
所以在x=0处可导
设f(x)在x=0处连续,且lim(x趋于0)f(x)/x存在,证明,f(x)在x=0处可导
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