求y=(x^2-3x+2)/(x^2+1)的渐近线求法

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求y=(x^2-3x+2)/(x^2+1)的渐近线求法

求y=(x^2-3x+2)/(x^2+1)的渐近线求法
求y=(x^2-3x+2)/(x^2+1)的渐近线求法

求y=(x^2-3x+2)/(x^2+1)的渐近线求法
ƒ(x) = (x² - 3x + 2)/(x² + 1)
= [(x² + 1) - 3x + 1]/(x² + 1)
= 1 + (1 - 3x)/(x² + 1)
lim(x→±∞) [ƒ(x) - 1]
= lim(x→±∞) [1 + (1 - 3x)/(x² + 1)] - 1
= lim(x→±∞) (1 - 3x)/(x² + 1)
= lim(x→±∞) (1/x² - 3/x)/(1 + 1/x²)
= 0/1 = 0
所以y = 1是水平渐近线,只有这么一条渐近线.

是吗我在呢么不知道

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