Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.5 Exercises - Page 89: 58

Answer

See explanation

Work Step by Step

When $v\rightarrow c$ from the left, we have $\frac{v}{c}\rightarrow !^-$ so $1-\frac{v^2}{c^2}\rightarrow 0^+$ We determine the limit: $\lim_{v\rightarrow c^-} m=\lim_{v\rightarrow c^-}\frac{m_0}{1-\frac{v^2}{c^2}}=\infty$ When the particle’s speed $v$ approaches the speed of light $c$, its relativistic mass increases without bound, so it would require infinite energy to accelerate the particle to the speed of light — hence, no object with mass can reach or exceed $c$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.