Vertical Asymptote

==2024-11-22

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Theory

$y=f(x)$ has a vertical Asymptote at x=a if, ${\lim }_{x\to a^{-}}=\pm \infty$, ${\lim }_{x\to a^{+}}=\pm \infty$

Examples

y=(x^2-1)/x
x=0

$f(x)=\frac{x^2-1}{x}$ Here, At $x\to 0^{+}$, $y\to -\infty$ , $x\to 0^{-}$, $y\to +\infty$ So, $x=0$ is the vertical asymptote of $f(x)$.

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PTR