Chapter 7.5, Problem 56AYU

To determine

a. Graph the function which can be used to approximate the smooth curve.

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

b. $f\left(x\right) = \frac{1}{2}\text{sin}2\pi x + \frac{1}{4}\text{sin}4\pi x + \frac{1}{8}\text{sin}8\pi x 0 \le x \le 4$ and compare the result to the graph obtained in part (a).

c. $f\left(x\right) = \frac{1}{2}\text{sin}2\pi x + \frac{1}{4}\text{sin}4\pi x + \frac{1}{8}\text{sin}8\pi x + \frac{1}{16}\text{sin}16\pi x 0 \le x \le 4.$ compare the result to the graph obtained in part (a).

d. What do you think the next approximation to the sawtooth curve is?