求二阶导数问题

2025-04-14 12:01:27
推荐回答(1个)
回答1:

lim(x->0) [ 1+x+ f(x)/x]^(1/x) =e^3

=>
x->0
f(x) ~ 2x^2
(1)
f(0) =0
(2)
f'(0)
=lim(h->0) [f(h)- f(0)]/h
=lim(h->0) f(h)/h
=lim(h->0) 2h^2/h
=lim(h->0) 2h
=0
(3)
f''(0)
=lim(h->0) [f'(h) -f'(0)]/ h
=lim(h->0) 4h/ h
=4