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

Answer 2

答案是2
洛比达法则 上下求导下面是x上面是你要求的再代入1，答案知道了吧！