Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.3 - Trigonometric Graphs - 5.3 Exercises - Page 430: 82

Answer

(a) this function is even. (b) $x=\pm\frac{\pi}{4}, \pm\frac{\pi}{2}, \pm\frac{3\pi}{4}, \pm \pi,\pm\frac{5\pi}{4},... $ (c) The graph of the function is shown in the figure. (d) As $x\to -\infty, f(x)\to 0$ and as $x\to \infty, f(x)\to 0$ (e) $x\to0, f(x)\to 2$

Work Step by Step

(a) $f(-x)=\frac{sin(-4x)}{-2x}=\frac{sin(4x)}{2x}==f(x)$, so this function is even. (b) Let $sin(4x)=0, x\ne0$, we can find the x-intercepts as $x=\pm\frac{\pi}{4}, \pm\frac{\pi}{2}, \pm\frac{3\pi}{4}, \pm \pi,\pm\frac{5\pi}{4},... $ (c) The graph of the function is shown in the figure. (d) As $x\to -\infty, f(x)\to 0$ and as $x\to \infty, f(x)\to 0$ (e) As $x\to 0$, both the numerator and the denominator approach zero, and the ratio approaches 2 ($x\to0, f(x)\to 2$) as shown in the graph.
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