91Ó°ÊÓ

Finding a Limit In Exercises \(47-62,\) find the limit. $$ \lim _{x \rightarrow 2} \frac{x^{2}+2 x-8}{x^{2}-x-2} $$

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. $$ \begin{array}{l}{f(x)=\frac{x-3}{x^{2}-4 x+3}} \\ {\lim _{x \rightarrow 3} f(x)}\end{array} $$

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? \ $$ f(x)=\left\\{\begin{array}{ll}{-2 x+3,} & {x<1} \\ {x^{2},} & {x \geq 1}\end{array}\right. $$

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. $$ \begin{array}{l}{f(x)=\frac{x-9}{\sqrt{x}-3}} \\ {\lim _{x \rightarrow 9} f(x)}\end{array} $$

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? \ $$ f(x)=\left\\{\begin{array}{ll}{\frac{1}{2} x+1,} & {x \leq 2} \\ {3-x} & {x>2}\end{array}\right. $$

Infinite Limit In your own words, describe the meaning of an infinite limit. Is \(\infty\) a real number?

Finding a Limit In Exercises \(47-62,\) find the limit. $$ \lim _{x \rightarrow 4} \frac{\sqrt{x+5}-3}{x-4} $$

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? \ $$ f(x)=\left\\{\begin{array}{ll}{-2 x,} & {x \leq 2} \\ {x^{2}-4 x+1,} & {x>2}\end{array}\right. $$

Finding a Limit In Exercises \(47-62,\) find the limit. $$ \lim _{x \rightarrow 3} \frac{\sqrt{x+1}-2}{x-3} $$

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. $$ \begin{array}{l}{f(x)=\frac{x-3}{x^{2}-9}} \\ {\lim _{x \rightarrow 3} f(x)}\end{array} $$