Question

已知f(x)二阶导数连续f(0)=f'(0)=0 f"(0)=3 求：如图

Answer 1

lim(x->0) 2f(x^2)/[3(sinx)^4]
=lim(x->0) 2f(x^2)/(3x^4) (0/0)
=lim(x->0) 4x.f'(x^2)/(12x^3)
=lim(x->0) f'(x^2)/(3x^2) (0/0)
=lim(x->0) 2x.f''(x^2)/(6x)
=lim(x->0) f''(x^2)/3
=f''(0)/3
=1

追问

这不对吧，我们老师给的答案是1啊

追答

我的也是
lim(x->0) 2f(x^2)/[3(sinx)^4]
=lim(x->0) 2f(x^2)/(3x^4) (0/0)
=lim(x->0) 4x.f'(x^2)/(12x^3)
=lim(x->0) f'(x^2)/(3x^2) (0/0)
=lim(x->0) 2x.f''(x^2)/(6x)
=lim(x->0) f''(x^2)/3
=f''(0)/3
=1