91Ó°ÊÓ

The given functions with limits are

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

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.

localid="1648276820143" $\underset{x→c}{\lim }f\left(x\right)=∞$

For example inlocalid="1648268818924" $\underset{x→0}{\lim }f\left(x\right)=∞$, function value reaches to infinity as x reaches to 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 inrole="math" localid="1648269054235" $\underset{x→∞}{\lim }f\left(x\right)=0$, function value reaches to zero as x reaches to infinity and horizontal asymptotes at$y=0.$