How do you find the slant asymptote of f(x) = (2x^2 + 3x + 8)/(x + 3)f(x)=2x2+3x+8x+3?

1 Answer
Roy D.
May 14, 2018

y = 2x-3

Explanation:

Use polynomial long division:
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Thus \frac{2x^2+3x+8}{x+3}=2x-3+\frac{17}{x+3}2x2+3x+8x+3=2x−3+17x+3
\lim_{x\to \infty } [2x-3+\frac{17}{x+3}]=2x-3
\lim_{x\to -\infty } [2x-3+\frac{17}{x+3}]=2x-3

Thus the obliques asymptote is y = 2x-3

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