Ean Chapman

2023-03-16

How to find vertical asymptotes using limits?

Wilhalm3qdn

Beginner2023-03-17Added 8 answers

The vertical line $x=a$ is a vertical asymptote of $f(x)$ if either

$\underset{x\to {a}^{-}}{lim}f\left(x\right)=\pm \infty$ or $\underset{x\to {a}^{+}}{lim}f\left(x\right)=\pm \infty$.

Thus, we must identify $a$-values such that either the left-hand limit or the right-hand limit is $\pm \infty$.

$\underset{x\to {a}^{-}}{lim}f\left(x\right)=\pm \infty$ or $\underset{x\to {a}^{+}}{lim}f\left(x\right)=\pm \infty$.

Thus, we must identify $a$-values such that either the left-hand limit or the right-hand limit is $\pm \infty$.

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