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I need to find the asymptotes of $y = \frac{2x^2 + 3x - 6}{2x + 1}$. The asymptote at $x = -1/2$ is clear. If one long divides they can easily see that there is an asymptote of $y = x + 1$ as $x$ goes to infinity.

However, what is wrong with this reasoning? I claim that as $x$ goes to infinity, the $2x^2$ term will dominate, so the graph will be on the order of $y = 2x^2$, which has no asymptote. So $y = x + 1$ is not an asymptote.

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    Did you forget about the denominator or something? By your reasoning, $x$ is $x^2/x$ so $x$ grows like $x^2$!2011-09-06
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    Thank you for making explicit what you are not understanding. It makes it easier to give an appropriate answer, as I think has been done. I hope they help.2011-09-06
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    @anon: well, $x^2!$ really does grow quite a bit... :) (Yes, I know what you meant to say.)2011-09-06

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