91Ó°ÊÓ

Finding a One-Sided Limit In Exercises \(33-48,\) find the one-sided limit (if it exists.). $$ \lim _{x \rightarrow-3} \frac{x+3}{x^{2}+x-6} $$

Evaluating Limits In Exercises \(37-40,\) use the information to evaluate the limits. $$ \begin{array}{l}{\lim _{x \rightarrow c} f(x)=3} \\ {\lim _{x \rightarrow c} g(x)=2} \\ {\text { (a) } \lim _{x \rightarrow c}[5 g(x)]} \\ {\text { (b) } \lim _{x \rightarrow c}[f(x)+g(x)]} \\ {\text { (d) } \lim _{x \rightarrow c}[f(x) g(x)]} \\ {\text { (d) } \lim _{x \rightarrow c} \frac{f(x)}{g(x)}}\end{array} $$

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? \ $$ f(x)=x^{2}-9 $$

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 \(L .\) $$ \lim _{x \rightarrow 4}(x+2) $$

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 \(L .\) $$ \lim _{x \rightarrow-2}(4 x+5) $$

Evaluating Limits In Exercises \(37-40,\) use the information to evaluate the limits. $$ \begin{array}{l}{\lim _{x \rightarrow c} f(x)=2} \\ {\lim _{x \rightarrow c} g(x)=\frac{3}{4}} \\ {\text { (a) } \lim _{x \rightarrow c}[4 f(x)]} \\\ {\text { (b) } \lim _{x \rightarrow c}[f(x)+g(x)]} \\ {\text { (c) } \lim _{x \rightarrow c}[f(x) g(x)]} \\ {\text { (d) } \lim _{x \rightarrow c} \frac{f(x)}{g(x)}}\end{array} $$

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

Finding a One-Sided Limit In Exercises \(33-48,\) find the one-sided limit (if it exists.). $$ \lim _{x \rightarrow(-1 / 2)^{+}} \frac{6 x^{2}+x-1}{4 x^{2}-4 x-3} $$

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

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 \(L .\) $$ \lim _{x \rightarrow-4}\left(\frac{1}{2} x-1\right) $$