91Ó°ÊÓ

In Exercises 15–22, use the graph to find the limit (if it exists). If the limit does not exist, explain why. $$ \lim _{x \rightarrow 2} \frac{|x-2|}{x-2} $$

Finding Vertical Asymptotes In Exercises \(13-28\) , find the vertical asymptotes (if any) of the graph of the function. $$ f(x)=\frac{3}{x^{2}+x-2} $$

Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow 1} \frac{x}{x^{2}+4} $$

Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow 1} \frac{3 x+5}{x+1} $$

In Exercises 15–22, use the graph to find the limit (if it exists). If the limit does not exist, explain why. $$ \lim _{x \rightarrow 5} \frac{2}{x-5} $$

Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow 1^{+}} f(x), \text { where } f(x)=\left\\{\begin{array}{ll}{x,} & {x \leq 1} \\ {1-x,} & {x>1}\end{array}\right. $$

Finding Vertical Asymptotes In Exercises \(13-28\) , find the vertical asymptotes (if any) of the graph of the function. $$ g(x)=\frac{x^{3}-8}{x-2} $$

Finding a Limit In Exercises \(7-26\) , find the limit (if it exists). If it does not exist, explain why. $$ \lim _{x \rightarrow \pi} \cot x $$

Finding Vertical Asymptotes In Exercises \(13-28\) , find the vertical asymptotes (if any) of the graph of the function. $$ f(x)=\frac{4 x^{2}+4 x-24}{x^{4}-2 x^{3}-9 x^{2}+18 x} $$

Finding a Limit In Exercises \(5-22,\) find the limit. $$ \lim _{x \rightarrow 7} \frac{3 x}{\sqrt{x+2}} $$