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Chapter 4: Problem 48
Find the length of the sides of a regular hexagon inscribed in a circle of radius 25 inches.
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Evaluate the expression without using a calculator. $$ \arcsin \frac{1}{2} $$
Consider the function given by \(f(x)=x-\cos x\) (a) Use a graphing utility to graph the function and verify that there exists a zero between 0 and 1 . Use the graph to approximate the zero. (b) Starting with \(x_{0}=1,\) generate a sequence \(x_{1}, x_{2},\) \(x_{3}, \ldots,\) where \(x_{n}=\cos \left(x_{n-1}\right) .\) For example, \(x_{0}=1\) $$ \begin{array}{l} x_{1}=\cos \left(x_{0}\right) \\ x_{2}=\cos \left(x_{1}\right) \\ x_{3}=\cos \left(x_{2}\right) \end{array} $$ \(\vdots\) What value does the sequence approach?
Evaluate the expression without using a calculator. $$ \arccos 0 $$
Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ h(x)=x \sin \frac{1}{x} $$
Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) \(x \rightarrow \frac{\pi^{+}}{2}\left(\right.\) as \(x\) approaches \(\frac{\pi}{2}\) from the right (b) \(x \rightarrow \frac{\pi^{-}}{2}\left(\right.\) as \(x\) approaches \(\frac{\pi}{2}\) from the left (c) \(x \rightarrow-\frac{\pi^{+}}{2}\left(\right.\) as \(x\) approaches \(-\frac{\pi}{2}\) from the right \()\) (d) \(x \rightarrow-\frac{\pi^{-}}{2}\left(\right.\) as \(x\) approaches \(-\frac{\pi}{2}\) from the left \()\) $$ f(x)=\sec x $$
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