lim(x趋向于0)f(2x)/x=1,且f(x)连续,则f'(0)=

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lim(x趋向于0)f(2x)/x=1,且f(x)连续,则f'(0)=

lim(x趋向于0)f(2x)/x=1,且f(x)连续,则f'(0)=
lim(x趋向于0)f(2x)/x=1,且f(x)连续,则f'(0)=

lim(x趋向于0)f(2x)/x=1,且f(x)连续,则f'(0)=
lim(x趋向于0)f(2x)/x=1,f(x)连续,则f(0)=0
f'(0)=lim [f(2x)-f(0)]/[2x-0]=lim f(2x)/(2x)=1/2

作变量变换 2x=t
则 x=t/2
当 x→0 时,t→0
lim(x趋向于0)f(2x)/x=1,
lim(t趋向于0)f(t)/(t/2)=1,
2*f'(0)=1
f'(0)=1/2