Chapter 1: Problem 16
In Exercises \(7-20,\) find the vertical asymptotes (if any) of the function. $$ f(z)=\ln \left(z^{2}-4\right) $$
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Use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in the interval [0, 1]. Repeatedly "zoom in" on the graph of the function to approximate the zero accurate to two decimal places. Use the zero or root feature of the graphing utility to approximate the zero accurate to four decimal places. $$ h(\theta)=1+\theta-3 \tan \theta $$
In Exercises 115 and \(116,\) find the point of intersection of the graphs of the functions. $$ \begin{array}{l} y=\arccos x \\ y=\arctan x \end{array} $$
In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 0^{-}}\left(x^{2}-\frac{2}{x}\right) $$
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. $$ f(x)=\frac{e^{-x}+1}{e^{x}-1} $$
True or False? In Exercises \(50-53\), determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Use the \(\varepsilon-\delta\) definition of infinite limits to prove that \(\lim _{x \rightarrow 3^{+}} \frac{1}{x-3}=\infty\)
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