Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 56

Answer

0, please see step-by-step,

Work Step by Step

Finding the limit: $\displaystyle \lim_{v\rightarrow c^{-}}(L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}})=L_{0}\sqrt{1-1}=0$ Interpretation: As the velocity approaches the speed of light, the length of the object approaches $0$. A left-sided limit is used because physically, the right sided limit is not defined, This is because velocity can not approach the speed of light from above (from the right): $v\rightarrow c^{+}$ means $v > c$, which can not be.
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