91Ó°ÊÓ

Graphical, Numerical, and Analytic Analysis In Exercises \(75-82\) , use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. $$ \lim _{x \rightarrow 0} \frac{\cos x-1}{2 x^{2}} $$

Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=x \sqrt{x+3} $$

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?

Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=\sec \frac{\pi x}{4} $$

Graphical, Numerical, and Analytic Analysis In Exercises \(75-82\) , use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. $$ \lim _{x \rightarrow 0} \frac{\sin x^{2}}{x} $$

Graphical, Numerical, and Analytic Analysis In Exercises \(75-82\) , use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. $$ \lim _{x \rightarrow 0} \frac{\sin x}{\sqrt[3]{x}} $$

Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=\cos \frac{1}{x} $$

Testing for Continuity In Exercises \(77-84\) , describe the interval(s) on which the function is continuous. $$ f(x)=\left\\{\begin{array}{ll}{\frac{x^{2}-1}{x-1},} & {x \neq 1} \\ {2,} & {x=1}\end{array}\right. $$

Finding a Limit In Exercises \(83-88\) , find \(\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\) $$ f(x)=3 x-2 $$

Finding a Limit In Exercises \(83-88\) , find \(\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\) $$ f(x)=-6 x+3 $$