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Chapter 0: Problem 49
Find an equation of the line satisfying the conditions. Write your answer in the slope-intercept form. Passes through \((2,4)\) and \((3,8)\)
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Find the exact value of the given expression. $$ \cos ^{-1} \frac{1}{2} $$
Determine whether \(h=g \circ f\) is even, odd, or neither, given that a. both \(g\) and \(f\) are even. b. \(g\) is even and \(f\) is odd. c. \(g\) is odd and \(f\) is even. d. both \(g\) and \(f\) are odd.
a. Plot the graph of \(f(x)=\cos (\sin x)\). Is \(f\) odd or even? b. Verify your answer to part (a) analytically.
Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=\sin x, \quad y=2 \sin \frac{x}{2}\)
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 \(x\).
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