91Ó°ÊÓ

Finding a Limit What is the limit of \(f(x)=4\) as \(x\) approaches \(\pi ?\)

One-Sided Limit In Exercises \(49-52\) , use a graphing utility to graph the function and determine the one-sided limit. $$ \begin{array}{l}{f(x)=\frac{x^{3}-1}{x^{2}+x+1}} \\ {\lim _{x \rightarrow 1^{-}} f(x)}\end{array} $$

Finding a Limit What is the limit of \(g(x)=x\) as \(x\) approaches \(\pi ?\)

Finding a Limit In Exercises \(47-62,\) find the limit. $$ \lim _{x \rightarrow 5} \frac{5-x}{x^{2}-25} $$

Removable and Nonremovable Discontinuities In Exercises \(35-60,\) find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? \ $$ f(x)=\frac{|x-5|}{x-5} $$

Finding a Limit In Exercises \(47-62,\) find the limit. $$ \lim _{x \rightarrow-3} \frac{x^{2}+x-6}{x^{2}-9} $$

Removable and Nonremovable Discontinuities In Exercises \(35-60,\) find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? \ $$ f(x)=\left\\{\begin{array}{ll}{x,} & {x \leq 1} \\ {x^{2},} & {x>1}\end{array}\right. $$

In Exercises 51–54, use a graphing utility to graph the function and estimate the limit (if it exists). What is the domain of the function? Can you detect a possible error in determining the domain of a function solely by analyzing the graph generated by a graphing utility? Write a short paragraph about the importance of examining a function analytically as well as graphically. $$ \begin{array}{l}{f(x)=\frac{\sqrt{x+5}-3}{x-4}} \\ {\lim _{x \rightarrow 4} f(x)}\end{array} $$

One-Sided Limit In Exercises \(49-52\) , use a graphing utility to graph the function and determine the one-sided limit. $$ \begin{array}{l}{f(x)=\frac{1}{x^{2}-25}} \\ {\lim _{x \rightarrow 5^{-}} f(x)}\end{array} $$

One-Sided Limit In Exercises \(49-52\) , use a graphing utility to graph the function and determine the one-sided limit. $$ \begin{array}{c}{f(x)=\sec \frac{\pi x}{8}} \\ {\lim _{x \rightarrow 4^{+}} f(x)}\end{array} $$