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Chapter 1: Problem 4
If the position function of a particle is \(x(t)=t^{2}+8 t, t>0,\) find the distance that the particle travels from \(t=0\) to \(t=4\) .
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Water is draining at the rate of 48\(\pi \mathrm{f}^{3} / \mathrm{second}\) from the vertex at the bottom of a conical tank whose diameter at its base is 40 feet and whose height is 60 feet. (a) Find an expression for the volume of water in the tank, in terms of its radius, at the surface of the water. (b) At what rate is the radius of the water in the tank shrinking when the radius is 16 feet? (c) How fast is the height of the water in the tank dropping at the instant that the radius is 16 feet?
\(\lim _{x \rightarrow 0} 4 \frac{\sin x \cos x-\sin x}{x^{2}}=\) (A) 2 (B) \(\frac{40}{3}\) (C) 0 (D) undefined
Find the area of the region between the two curves in each problem, and be sure to sketch each one. (We gave you only endpoints in one of them) The answers are in Chapter 19 . The curve \(y=x^{3}\) and the \(x\) -axis, from \(x=-1\) to \(x=2\).
Evaluate the following integrals. \(\int \frac{e^{x}+e^{-x}}{e^{x}-e^{-x}} d x\)
Evaluate the following integrals. \(\int x 4^{-x^{2}} d x\)
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