Question

如果f′(1)=2,求limf(1+h)-f(1-2h)/e^2h-1 h趋向于0

Answer 1

分母等价于2h,因此原极限【lim f(1+h)－f(1－2h)】/2h=lim {【f(1+h)－f(0)】/2h+【f(0)－f(1－2h)】/2h}=0.5f‘(0)+f'(0)=1.5f'(0).