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

Jun 8, 2018

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

#### Explanation:

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