91Ó°ÊÓ

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

In Exercises 27 and 28, sketch a graph of a function that satisfies the given values. (There are many correct answers.) $$ \begin{array}{l}{f(-2)=0} \\ {f(2)=0} \\ {\lim _{x \rightarrow-2} f(x)=0} \\\ {\lim _{x \rightarrow 2} f(x) \text { does not exist. }}\end{array} $$

Continuity of a Function In Exercises \(27-30,\) discuss the continuity of each function. $$ f(x)=\frac{1}{2}[ | x] ]+x $$

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 1} \cos \frac{\pi x}{3} $$

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

Finding a Limit of a Trigonometric Function In Exercises \(27-36,\) find the limit of the trigonometric function. $$ \lim _{x \rightarrow 2} \sin \frac{\pi x}{2} $$

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. $$ f(x)=\frac{x^{2}-2 x-8}{x+1} $$

Continuity of a Function In Exercises \(27-30,\) discuss the continuity of each function. $$ f(x)=\left\\{\begin{array}{ll}{x,} & {x<1} \\ {2,} & {x=1} \\ {2 x-1,} & {x>1}\end{array}\right. $$

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

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