一道微积分题目,请高手们教教我.设f(x)在x=1处连续,且lim(x趋向于1)f(x)/x-1=2,则f'(x)是多少?

Question

一道微积分题目,请高手们教教我.
设f(x)在x=1处连续,且lim(x趋向于1)f(x)/x-1=2,则f'(x)是多少?

Answer 1

∴ lim(x->1) f(x)/(x-1) = 2
∵ f(x)在x=1处连续 ,
∴
f(1) = lim(x->1) f(x) = lim(x->1) (x-1)*f(x)/(x-1) = 0*2 = 0
∴
f'(1) = lim(x->1) [ f(x) - f(1) ] /(x-1)
= lim(x->1) f(x) /(x-1)
= 2