91Ó°ÊÓ

Determine whether the function is even, odd, or neither. Use a graphing utility to verify your result. $$ f(x)=\sqrt[3]{x} $$

Prove that if the slopes of two nonvertical lines are negative reciprocals of each other, then the lines are perpendicular.

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

Find \(\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}\). $$ f(x)=x^{2}-4 x $$

Use the properties of logarithms to expand the logarithmic expression. $$ \ln \sqrt[3]{z+1} $$

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

True or False? In Exercises \(57-60,\) determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f\) is undefined at \(x=c,\) then the limit of \(f(x)\) as \(x\) approaches \(c\) does not exist.

Use the properties of logarithms to expand the logarithmic expression. $$ \ln \left(\frac{x^{2}-1}{x^{3}}\right)^{3} $$

Use the Squeeze Theorem to find \(\lim _{x \rightarrow c} f(x)\). $$ c=0 ; 4-x^{2} \leq f(x) \leq 4+x^{2} $$

\( \text { True or False? } \) Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The lines represented by \(a x+b y=c_{1}\) and \(b x-a y=c_{2}\) are perpendicular. Assume \(a \neq 0\) and \(b \neq 0\).