设f(x)在x.处可导,且lim(x→0)x/[f(x.-2x)-f(x.)]=1/4,则f′(x.)等于多少?

问题描述:

设f(x)在x.处可导,且lim(x→0)x/[f(x.-2x)-f(x.)]=1/4,则f′(x.)等于多少?

lim(x→0)[f(x.-2x)-f(x.)]/x
=-2lim(2x→0)[f(x.)-f(x.-2x)]/2x
=-2lim(x→0)[f(x.)-f(x.-x)]/x
=-2f'(x)=1/4

f'(x)=-1/8
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