91Ó°ÊÓ

Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ \begin{array}{ll}{\text { Function }} & {\text { Interval }} \\\ {g(x)=\sqrt{49-x^{2}}} & {[-7,7]}\end{array} $$

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

Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ f(t)=3-\sqrt{9-t^{2}} \quad[-3,3] $$

Vertical Asymptote or Removable Discontinuity. In Exercises \(29-32\) , determine whether the graph of the function has a vertical asymptote or a removable discontinuity at \(x=-1 .\) Graph the function using a graphing utility to confirm your answer. $$ f(x)=\frac{\sin (x+1)}{x+1} $$

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 \(0<|x-c|<\delta .\) $$ \lim _{x \rightarrow 2}(3 x+2) $$

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 5 \pi / 6} \sin x $$

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

Continuity on a closed Interval In Exercises 31-34, discuss the continuity of the function on the closed interval. $$ f(x)=\left\\{\begin{array}{ll}{3-x,} & {x \leq 0} \\ {3+\frac{1}{2} x,} & {x>0}\end{array} \quad[-1,4]\right. $$

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 5 \pi / 3} \cos x $$

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 \(0<|x-c|<\delta .\) $$ \lim _{x \rightarrow 6}\left(6-\frac{x}{3}\right) $$