f `(1)=-2,求lim h接近于0 f(1+2h)-f(1) / h 详细过程
问题描述:
f `(1)=-2,求lim h接近于0 f(1+2h)-f(1) / h 详细过程
答
lim(h->0)[f(1+2h)-f(1)/h=lim(h->0)[f'(1+2h)*2-f'(1)/h' (罗比达法则)
=lim(h->0)[f'(1+2h)*2-f'(1)=lim(h->0)[f'(1+2h)*2-lim(h->0)f'(1)=0
答
lim h→0 [f(1+2h)-f(1)] / h
=2lim 2h→0 [f(1+2h)-f(1)] / (2h)
=2f'(1)
=-4