求助吧友..

x->0
ln(1+2x)= 2x -(1/2)(2x)^2 +o(x^2) =2x -2x^2+o(x^2)
xf(x) = f(0)x+f'(0)x^2 +o(x^2)
ln(1+2x)+xf(x) = (2+f(0))x +(-2+f'(0))x^2 +o(x^2)
lm(x->0)[ln(1+2x)+xf(x)]/x^2 =1
=>
2+f(0)=0 and -2+f'(0)=1
f(0)=-2 and f'(0)=3
lim(x->0) (2+f(x))/x
=lim(x->0) f'(0)x/x
=f'(0)
=3
ans: C