limx->∞ [(xsinx(2/x) + (2/x)sinx] 是多少?

问题描述:

limx->∞ [(xsinx(2/x) + (2/x)sinx] 是多少?

令t=1/x t→0
limx->∞ [(xsin(2/x) + (2/x)sinx]
=limt→0[(sin2t)/t] + limx→∞(2/x)sinx
=2+0
=2