一个问题求解

x->0
sin6x =6x-(1/6)(6x)^3 +o(x^3) = 6x-36x^3 +o(x^3)
f(x)= f(0)+f'(0)x+(1/2)f''(0)x^2+o(x^2)
xf(x)= f(0)x+f'(0)x^2+(1/2)f''(0)x^3+o(x^3)
sin6x+xf(x) =[6+f(0)]x+ f'(0)x^2 +[-36+(1/2)f''(0)]x^3+o(x^3)
lim(x->0) [sin6x +xf(x)]/x^3 =0
lim(x->0) {[6+f(0)]x+ f'(0)x^2 +[-36+(1/2)f''(0)]x^3}/x^3 =0
=>
6+f(0)=0, f'(0)=0, -36+(1/2)f''(0)=0
f(0)=-6, f'(0)=0, (1/2)f''(0)=36
lim(x->0) [6+f(x)]/x^2
=lim(x->0) [6+f(0)+f'(0)x+(1/2)f''(0)x^2]/x^2
=lim(x->0) 36x^2/x^2
=36