91Ó°ÊÓ

Use an infinite series to approximate the indicated number accurate to three decimal places. \(\sin (0.5)\)

Find the rational number represented by the given repeating decimal. \(0.25252525 \ldots\)

Derive the series for tan \(x\) listed in Example 3 by long division of the Maclaurin series of \(\cos x\) into the Maclaurin series of \(\sin x\).

A ball with bounce coefficient \(r=0.64\) (see Problem 64) is dropped from an initial height of \(a=4 \mathrm{ft}\). Use a geometric series to compute the total time required for it to complete its infinitely many bounces. The time required for a ball to drop \(h\) feet (from rest) is \(\sqrt{2 h / g}\) seconds, where \(g=32 \mathrm{ft} / \mathrm{s}^{2}\).