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Chapter 0: Problem 15
Find the angle of inclination of a line with the given slope. You may use a calculator. $$ -1 $$
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Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=|x|, \quad y=2|x+1|-1\)
Find the inverse of \(f .\) Then use a graphing utility to plot the graphs of \(f\) and \(f^{-1}\) using the same viewing window. $$ f(x)=\frac{x}{\sqrt{x^{2}+1}}, \quad-1 \leq x \leq 1 $$
Let \(f(x)=2 x^{3}-5 x^{2}+x-2\) and \(g(x)=2 x^{3}\). a. Plot the graph of \(f\) and \(g\) using the same viewing window: \([-5,5] \times[-5,5]\). b. Plot the graph of \(f\) and \(g\) using the same viewing window: \([-50,50] \times[-100,000,100,000] .\) c. Explain why the graphs of \(f\) and \(g\) that you obtained in part (b) seem to coalesce as \(x\) increases or decreases without bound. Hint: Write \(f(x)=2 x^{3}\left(1-\frac{5}{2 x}+\frac{1}{2 x^{2}}-\frac{1}{x^{3}}\right)\) and study its behavior for large values of \(x\).
Plot the graph of the function \(f\) in an appropriate viewing window. (Note: The answer is not unique.) $$ f(x)=2 x^{4}-3 x^{3}+5 x^{2}-20 x+40 $$
Find the exact value of the given expression. $$ \tan ^{-1} \sqrt{3} $$
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