limx趋向0,∫上极限x下极限0costdt/x^2怎么做?
问题描述：
limx趋向0,∫上极限x下极限0costdt/x^2怎么做?
答
(x->0) lim ∫ costdt / x^2 [t:0,x]
=(x->0) lim ∫ d(sint) / x^2 [t:0,x]
=(x->0) lim sint / x^2 [t:0,x]
=(x->0) lim (sinx-sin0) / x^2
=(x->0) lim sinx / x^2
=(x->0) lim sinx / x * (x->0)lim 1/x
=1* (x->0)lim 1/x
是发散的,无极限