若函数f(x)在x=0处可导，分别求a、b的值

Question

如题所述

Answer 1

f(x)
=ln(1+x^2)/x ; x>0
=ax+b ; x≤0
f(0+)= lim(x->0) ln(1+x^2)/x =0
f(0)=f(0-)=lim(x->0) (ax+b) =b
f(0)=f(0+)=f(0-)
=>b=0
f'(0-)
=lim(h->0) [ah -f(0) ]/h
=lim(h->0) ah/h
=a
f'(0+)
=lim(h->0) [ln(1+h^2)/h -f(0) ]/h
=lim(h->0) ln(1+h^2)/h^2
=1
f'(0-)=f'(0+)
=>a=1
(a,b)=(1,0)本回答被网友采纳