Chapter 4: Problem 18
\(x^{4}-2=0\)
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Tolerance (a) About how accurately must the interior diameter of a 10 -m high cylindrical storage tank be measured to calculate the tank's volume to within 1\(\%\) of its true value? (b) About how accurately must the tank's exterior diameter be measured to calculate the amount of paint it will take to paint the side of the tank to within 5\(\%\) of the true amount?
Moving Ships Two ships are steaming away from a point \(O\) along routes that make a \(120^{\circ}\) angle. Ship \(A\) moves at 14 knots (nautical miles per hour; a nautical mile is 2000 yards). Ship \(B\) moves at 21 knots. How fast are the ships moving apart when \(O A=5\) and \(O B=3\) nautical miles? 29.5 knots
Multiple Choice If \(a<0,\) the graph of \(y=a x^{3}+3 x^{2}+\) \(4 x+5\) is concave up on (A) \(\left(-\infty,-\frac{1}{a}\right)\) (B) \(\left(-\infty, \frac{1}{a}\right)\) (C) \(\left(-\frac{1}{a}, \infty\right) (D) \)\left(\frac{1}{a}, \infty\right)\( (E) \)(-\infty,-1)$
$$ \begin{array}{l}{\text { Multiple Choice All of the following functions satisfy the }} \\ {\text { conditions of the Mean Value Theorem on the interval }[-1,1]} \\ {\text { except } }\end{array} $$ \((\mathbf{A}) \sin x\) \((\mathbf{B}) \sin ^{-1} x\) \((\mathrm{C}) x^{5 / 3}\) (D) \(x^{3 / 5}\) (E) \(\frac{x}{x-2}\)
Let \(y=f(x)=x^{3}-4 x\) If \(d x / d t=-2 \mathrm{cm} / \mathrm{sec},\) find \(d y / d t\) at the point where (a) \(x=-3 . \quad\) (b) \(x=1 . \quad\) (c) \(x=4\)
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