Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.1 Limits (An Intuitive Approach) - Exercises Set 1.1 - Page 61: 31

Answer

a. $l_o$ is the length of the rod at a speed of 0. b. $\lim_{v \to c^-} l(v) = 0$. The physical significance is that as the rod approaches the speed of light, its length approaches 0.

Work Step by Step

a. The function $l(v)$ is the length of a narrow rod as a function of $v$. Therefore, $l_0$ is the length of a narrow rod with $v=0$, or at a speed of $0$. b. From Fig. Ex-31 given in the problem, $l$ approaches 0 as $v$ approaches $c$ from the left. Thus, $\lim_{v \to c^-} l(v) = 0$. The physical significance is that as the rod approaches the speed of light, its length approaches 0.
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