lim(x→0)[tan(2x+x^3)/sin(x-x^2)] 和lim(x→0)[(x-sinx)/(x+sinx)]的答案和解法

问题描述:

lim(x→0)[tan(2x+x^3)/sin(x-x^2)] 和lim(x→0)[(x-sinx)/(x+sinx)]的答案和解法
如果错了请教教我怎麽解和解的过程.

第一题利用等价无穷小法则
lim(x→0)[tan(2x+x^3)/sin(x-x^2)]
=lim(x→0)[(2x+x^3)/(x-x^2)]=0
第二题分子分母同时除以x
lim(x→0)[(x-sinx)/(x+sinx)]
=lim(x→0)[(1-(sinx/x))/(1+(sinx/x))]然后利用等价无穷小
=lim(x→0)[(1-1)/(1+1)]=0