x趋向于无穷时 lim (3x-1)/(x^3 乘以 sin(1/x^2 ))

问题描述:

x趋向于无穷时 lim (3x-1)/(x^3 乘以 sin(1/x^2 ))

令t=1\x
原式=limt→0 ( 3/t-1)/(1/t * sin t^2)
=limt→0 ( 3/t-1)/(1/t * t^2) -----这里用到无穷小量有关知识
=limt→0 (3-t)
=3