91Ó°ÊÓ

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? \ $$ f(x)=\frac{1}{4-x^{2}} $$

Finding a One-Sided Limit In Exercises \(33-48,\) find the one-sided limit (if it exists.). $$ \lim _{x \rightarrow 0^{-}}\left(1+\frac{1}{x}\right) $$

Finding a One-Sided Limit In Exercises \(33-48,\) find the one-sided limit (if it exists.). $$ \lim _{x \rightarrow 0^{+}}\left(6-\frac{1}{x^{3}}\right) $$

Evaluating Limits In Exercises \(37-40,\) use the information to evaluate the limits. $$ \begin{array}{l}{\lim _{x \rightarrow c} f(x)=27} \\ {\text { (a) } \lim _{x \rightarrow c} \sqrt[3]{f(x)}} \\ {\text { (b) } \lim _{x \rightarrow c} \frac{f(x)}{18}} \\ {\text { (c) } \lim _{x \rightarrow c}[f(x)]^{2}} \\\ {\text { (d) } \lim _{x \rightarrow c}[f(x)]^{2 / 3}}\end{array} $$

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? \ $$ f(x)=\frac{1}{x^{2}+1} $$

Using the \(\varepsilon-\delta\) Definition of Limit In Exercises \(37-48\) , find the limit \(L\) . Then use the \(\varepsilon-\delta\) definition to prove that the limit is \(L .\) $$ \lim _{x \rightarrow 3}\left(\frac{3}{4} x+1\right) $$

Finding a Limit In Exercises \(41-46,\) write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. $$ \lim _{x \rightarrow 0} \frac{x^{2}+3 x}{x} $$

Using the \(\varepsilon-\delta\) Definition of Limit In Exercises \(37-48\) , find the limit \(L\) . Then use the \(\varepsilon-\delta\) definition to prove that the limit is \(L .\) $$ \lim _{x \rightarrow 6} 3 $$

Finding a One-Sided Limit In Exercises \(33-48,\) find the one-sided limit (if it exists.). $$ \lim _{x \rightarrow-4^{-}}\left(x^{2}+\frac{2}{x+4}\right) $$

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? \ $$ f(x)=3 x-\cos x $$