Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?

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Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?
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Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?
Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?

Lim(x趋向2)(x^3+2x^2)/(x-2)^2怎么做?
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

分子分母同除以x^2
原式=lim(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

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