求极限lim(x→∞) (1/(x-2)-12/(x³-8))要过程

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求极限lim(x→∞)(1/(x-2)-12/(x³-8))要过程求极限lim(x→∞)(1/(x-2)-12/(x³-8))要过程求极限lim(x→∞)(1/(x-2)-12/(

求极限lim(x→∞) (1/(x-2)-12/(x³-8))要过程
求极限lim(x→∞) (1/(x-2)-12/(x³-8))要过程

求极限lim(x→∞) (1/(x-2)-12/(x³-8))要过程
lim(x→∞) (1/(x-2)-12/(x³-8))
=lim(x→∞) ((x²+2x+4)/(x³-8)-12/(x³-8))
=lim(x→∞) (x²+2x-8)/(x³-8)
上下同除x³
则原式=lim(x→∞) (1/x+2/x²-8/x³)/(1-8/x³)
=0/(1-0)
=∞

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