求(2x^2-6x+5)/(x^3-8x^2+1)趋近于无穷大的极限

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求(2x^2-6x+5)/(x^3-8x^2+1)趋近于无穷大的极限
求(2x^2-6x+5)/(x^3-8x^2+1)趋近于无穷大的极限

求(2x^2-6x+5)/(x^3-8x^2+1)趋近于无穷大的极限
你好!
对于(多项式除以多项式)在x趋于无穷时的极限
1、分子次数高于分母次数:极限不存在(趋于无穷)
2、分子分母次数相等:极限等于最高次数项系数的比值
例如 lim(x→无穷) (x^2+1)/(2x^2 - x) = 1/2
3、分母次数高于分子次数:极限为0,例如本题.
故本题答案是0.
要过程很简单,分子分母同除以x^3,得到分子趋于0,分母趋于1.故极限为0.

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