91Ó°ÊÓ

Determine the limit of the trigonometric function (if it exists). $$ \lim _{\phi \rightarrow \pi} \phi \sec \phi $$

Use a graphing utility to graph the function on the interval \([-4,4] .\) Does the graph of the function appear continuous on this interval? Is the function continuous on \([-4,4] ?\) Write a short paragraph about the importance of examining a function analytically as well as graphically. $$ f(x)=\frac{x^{3}-8}{x-2} $$

Explain why the function has a zero in the given interval. $$\begin{array}{ll} \text { Function } & \text { Interval } \end{array}$$ $$ f(x)=\frac{1}{16} x^{4}-x^{3}+3 $$ $$ [1,2] $$

Use the \(\varepsilon-\delta\) definition of infinite limits to prove the statement. \(\lim _{x \rightarrow 3^{+}} \frac{1}{x-3}=\infty\)

Determine the limit of the trigonometric function (if it exists). $$ \lim _{x \rightarrow \pi / 2} \frac{\cos x}{\cot x} $$

Explain why the function has a zero in the given interval. $$\begin{array}{ll} \text { Function } & \text { Interval } \end{array}$$ $$ f(x)=x^{3}+3 x-2 $$ $$ [0,1] $$

Determine the limit of the trigonometric function (if it exists). $$ \lim _{x \rightarrow \pi / 4} \frac{1-\tan x}{\sin x-\cos x} $$

Use the \(\varepsilon-\delta\) definition of infinite limits to prove the statement. \(\lim _{x \rightarrow 4^{-}} \frac{1}{x-4}=-\infty\)

A right circular cone has base of radius 1 and height \(3 .\) A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube?

Explain why the function has a zero in the given interval. $$\begin{array}{ll} \text { Function } & \text { Interval } \end{array}$$ $$ f(x)=x^{2}-2-\cos x \quad[0, \pi] $$