Chapter 1: Problem 34
In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 1 / 2} x^{2} \tan \pi x $$
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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 \(\lim _{x \rightarrow 3^{+}} \frac{1}{x-3}=\infty\)
In Exercises \(35-38\), use a graphing utility to graph the function and determine the one-sided limit. $$ \begin{array}{l} f(x)=\frac{x^{3}-1}{x^{2}+x+1} \\ \lim _{x \rightarrow 1^{-}} f(x) \end{array} $$
Prove that if a function has an inverse function, then the inverse function is unique.
A dial-direct long distance call between two cities costs \(\$ 1.04\) for the first 2 minutes and \(\$ 0.36\) for each additional minute or fraction thereof. Use the greatest integer function to write the cost \(C\) of a call in terms of time \(t\) (in minutes). Sketch the graph of this function and discuss its continuity.
(a) Let \(f_{1}(x)\) and \(f_{2}(x)\) be continuous on the closed interval \([a,
b]\). If \(f_{1}(a)
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