这道高数用洛必达法则求极限的题怎么做

Question

如题所述

Answer 1

lim(h->0){ [f(a+h) -f(a)]/h - f'(a) }/h
=lim(h->0) [ f(a+h) -f(a) - hf'(a) ]/h^2 (0/0分子分母分别求导)
=lim(h->0) [ f'(a+h) - f'(a) ]/(2h)
=(1/2)lim(h->0) [ f'(a+h) - f'(a) ]/h
=(1/2)f''(a)