Question

Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?

Answer 1

因为lim(x趋向2)(x-2)^2/(x^3+2x^2)=0/16,所以由无穷小与无穷大的关系得,lim(x趋向2)(x^3+2x^2)/(x-2)^2=正无穷

Answer 2

分子分母同除以x^2
原式=lim<x→2>(x+2)/(1- 2/x)^2
分子→4，分母→0
lim[x^3+2x^2/(x-2)^2]=lim[(x^3+2x^2)/(x^2-4x+4]
=lim(3x^2+4x)/(2x-4),(上下求导）
=lim(6x+4)/2,(同上）
=(6x2+4)/2
=8