Chapter 8.5, Problem 56AE

The Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes.

(a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve.(a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve.

$f\left(x\right)=\frac{1}{2}\sin \left(2\pi x\right)+\frac{1}{4}\sin \left(4\pi x\right)0\le x\le 4$

(b) A better approximation to the sawtooth curve is given by

$f\left(x\right)=\frac{1}{2}\sin \left(2\pi x\right)+\frac{1}{4}\sin \left(4\pi x\right)+\frac{1}{8}\sin \left(8\pi x\right)$

Use a graphing utility to graph this function for $0\le x\le 4$ and compare the result to the graph obtained in part (a).

(c) A third and even better approximation to the sawtooth curve is given by

$f\left(x\right)=\frac{1}{2}\sin \left(2\pi x\right)+\frac{1}{4}\sin \left(4\pi x\right)+\frac{1}{8}\sin \left(8\pi x\right)+\frac{1}{16}\sin \left(16\pi x\right)$

Use a graphing utility to graph this function for $0\le x\le 4$ and compare the result t