Chapter 4: Problem 42
The volume of a sphere with radius 8\(\pm 0.3\) in.
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Multiple Choice Two positive numbers have a sum of 60. What is the maximum product of one number times the square of the second number? (a) 3481 (b) 3600 (c) 27,000 (d) 32,000 (e) 36,000
Growing Sand Pile Sand falls from a conveyor belt at the rate of 10 \(\mathrm{m}^{3} / \mathrm{min}\) onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the (a) height and (b) radius changing when the pile is 4 \(\mathrm{m}\) high? Give your answer in \(\mathrm{cm} / \mathrm{min.}\)
Writing to Learn The function $$ f(x)=\left\\{\begin{array}{ll}{x,} & {0 \leq x<1} \\ {0,} & {x=1}\end{array}\right. $$ is zero at \(x=0\) and at \(x=1 .\) Its derivative is equal to 1 at every point between 0 and \(1,\) so \(f^{\prime}\) is never zero between 0 and 1 and the graph of \(f\) has no tangent parallel to the chord from \((0,0)\) to \((1,0) .\) Explain why this does not contradict the Mean Value Theorem.
Multiple Choice If the linearization of \(y=\sqrt[3]{x}\) at \(x=64\) is used to approximate \(\sqrt[3]{66},\) what is the percentage error? \(\begin{array}{llll}{\text { (A) } 0.01 \%} & {\text { (B) } 0.04 \%} & {\text { (C) } 0.4 \% \text { (D) 1 } \%}\end{array}\) (E) 4\(\%\)
Writing to Learn Explain why there is a zero of \(y=\cos x\) between every two zeros of \(y=\sin x .\)
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