What are the asymptotes of $f (x) = \frac{x^{2}}{{(x - 2)}^{2}}$ $f(x)=x^2/(x-2)^2$ ?

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What are the asymptotes of $f (x) = \frac{x^{2}}{{(x - 2)}^{2}}$ $f(x)=x^2/(x-2)^2$ ?

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Answer 1 · 2018-06-08T16:21:06

$\frac{x^{2}}{{(x - 2)}^{2}} \to 1$ $x^2/(x-2)^2 ->1$ for
$x \to \pm \infty$ $x-> pm infty$
$\frac{x^{2}}{{(x - 2)}^{2}} \to \infty$ $x^2/(x-2)^2->infty$ for $x \to 2$ $x->2$

Explanation:

writing
$\frac{x^{2}}{x^{2} - 4 x + 4} = \frac{1}{1 - \frac{4}{x} + \frac{4}{x^{2}}} \to 1$ $x^2/(x^2-4x+4)=1/(1-4/x+4/x^2)->1$ for $x \to \pm \infty$ $x->pm infty$
$\frac{x^{2}}{{(x - 2)}^{2}} \to \infty$ $x^2/(x-2)^2->infty$ for $x \to 2$ $x->2$

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What are the asymptotes of $f (x) = \frac{x^{2}}{{(x - 2)}^{2}}$ $f(x)=x^2/(x-2)^2$ ?

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What are the asymptotes of f(x)=x^2/(x-2)^2f(x)=x2(x−2)2f(x)=x^2/(x-2)^2?

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What are the asymptotes of $f (x) = \frac{x^{2}}{{(x - 2)}^{2}}$ $f(x)=x^2/(x-2)^2$ ?