91Ó°ÊÓ

Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ g(x)=\frac{1}{x^{2}-4} \quad \quad \quad[-1,2] $$

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

Finding a \(\delta\) for a Given \(\varepsilon\) In Exercises \(33-36\) , find the limit \(L\) . Then find \(\delta>0\) such that \(|f(x)-L|<0.01\) whenever \(0<|x-c|<\delta .\) $$ \lim _{x \rightarrow 2}\left(x^{2}-3\right) $$

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? \ $$ f(x)=\frac{6}{x} $$

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

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 3} \tan \left(\frac{\pi x}{4}\right) $$

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

Finding a \(\delta\) for a Given \(\varepsilon\) In Exercises \(33-36\) , find the limit \(L\) . Then find \(\delta>0\) such that \(|f(x)-L|<0.01\) whenever \(0<|x-c|<\delta .\) $$ \lim _{x \rightarrow 4}\left(x^{2}+6\right) $$

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 7} \sec \left(\frac{\pi x}{6}\right) $$

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? \ $$ f(x)=\frac{4}{x-6} $$