求极限 lim(x→0) (∫上限x눀下限0 sintdt)⼀xsin대x

2025-01-20 04:41:23
推荐回答(1个)
回答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