Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 93: 30

Answer

(a) When we zoom in toward the point where the graph crosses the y-axis, we can estimate that $\lim\limits_{x \to 0}f(x) = 0.32$ (b) $\lim\limits_{x \to 0}f(x) = 0.32$
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Work Step by Step

(a) When we zoom in toward the point where the graph crosses the y-axis, we can estimate that $\lim\limits_{x \to 0}f(x) = 0.32$ (b) We can evaluate $f(x)$ for values of $x$ that approach $0$: $f(0.1) = \frac{sin~0.1}{sin~(0.1~\pi)} = 0.32$ $f(-0.1) = \frac{sin~-0.1}{sin~(-0.1~\pi)} = 0.32$ $f(0.01) = \frac{sin~0.01}{sin~(0.01~\pi)} = 0.32$ $f(-0.01) = \frac{sin~-0.01}{sin~(-0.01~\pi)} = 0.32$ $f(0.001) = \frac{sin~0.001}{sin~(0.001~\pi)} = 0.32$ $f(-0.001) = \frac{sin~-0.001}{sin~(-0.001~\pi)} = 0.32$ $f(0.0001) = \frac{sin~0.0001}{sin~(0.0001~\pi)} = 0.32$ $f(-0.0001) = \frac{sin~-0.0001}{sin~(-0.0001~\pi)} = 0.32$ $f(0.00001) = \frac{sin~0.00001}{sin~(0.00001~\pi)} = 0.32$ $f(-0.00001) = \frac{sin~-0.00001}{sin~(-0.00001~\pi)} = 0.32$ We can see that $\lim\limits_{x \to 0}f(x) = 0.32$
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