求极限 lim(x→0) (∫上限x²下限0 sintdt)/xsin³x

Question

如题所述

Answer 1

x->0
sinx ~ x

lim(x->0) (∫(0->x^2) sint dt)/ [x(sinx)^3]
=lim(x->0) (∫(0->x^2) sint dt)/ x^4 (0/0)
=lim(x->0)2xsin(x^2)/ (4x^3)
=lim(x->0)2x^3/ (4x^3)
=1/2本回答被提问者采纳