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Chapter 4: Problem 25
Use a calculator to evaluate the expression. Round your result to two decimal places. $$\arctan (-3)$$
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Sketch a graph of the function. $$g(t)=\arccos (t+2)$$
Consider the functions \(f(x)=\sin x\) and \(f^{-1}(x)=\arcsin x\). (a) Use a graphing utility to graph the composite functions \(f \circ f^{-1}\) and \(f^{-1} \circ f\). (b) Explain why the graphs in part (a) are not the graph of the line \(y=x .\) Why do the graphs of \(f \circ f^{-1}\) and \(f^{-1}\) o \(f\) differ?
Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\) (a) \(x \rightarrow\left(\frac{\pi}{2}\right)^{+}\) (b) \(x \rightarrow\left(\frac{\pi}{2}\right)^{-}\) (c) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{+}\) (d) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{-}\) $$f(x)=\sec x$$
Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow \infty, \text { the value of } \arctan x \rightarrow\text { _____ } .$$
Use a graphing utility to graph the functions \(f(x)=\sqrt{x}\) and \(g(x)=6\)
arctan \(x .\) For \(x>0,\) it appears that \(g>f .\) Explain why you know that
there exists a positive real number \(a\) such that \(g
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