91Ó°ÊÓ

Vertical Asymptotes

Horizontal Asymptotes

Vertical Asymptotes: If f is a function and c and L are real numbers where the value of $f\left(x\right)$reaches infinity as x reaches c then we can say that infinity is the limit of $f\left(x\right)$as x approaches cand $x=c$is vertical asymptotes.

$\underset{x→c}{\lim }f\left(x\right)=∞$

For example inrole="math" localid="1648276958501" $\underset{x→0}{\lim }\frac{1}{x}=∞$, function value reaches infinity as x reaches zero and vertical asymptotes at$x=0$.

Horizontal Asymptotes: If f is a function and c and L are real numbers where the value of $f\left(x\right)$reaches L as x reaches infinity then we can say that L is the limit of $f\left(x\right)$as x approaches infinity and $y=L$is horizontal asymptotes.

$\underset{x→∞}{\lim }f\left(x\right)=L$

For example in$\underset{x→∞}{\lim }\frac{1}{x}=0$, function value reaches zero as x reaches infinity and horizontal asymptotes at$y=0$.