微积分重要极限题

Question

第二题为什么有负号
第三题是不是正确的呢

Answer 1

Answer 2

lim(h->0) [f(x0+h)/f(x0) ]^(1/h)
=lim(h->0) e^{ (ln[f(x0+h)/f(x0) ]) / h }
=lim(h->0) e^{ [ lnf(x0+h)-lnf(x0) ] / h } (0/0 分子分母分别求导)
=lim(h->0) e^{ [ f'(x0+h)/f(x0+h) ]
= e^[ f'(x0)/f(x0) ]
or
h->0
f(x0+h) = f(x0) +f'(x0)h +o(h)
lim(h->0) [f(x0+h)/f(x0) ]^(1/h)
=lim(h->0){ [ f(x0) +f'(x0)h] /f(x0) }^(1/h)
=lim(h->0) { 1 +[f'(x0)/f(x0)]h }^(1/h)
=e^[f'(x0)/f(x0)]本回答被网友采纳