Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 13

Answer

Prove that $\lim\limits_{v\to1}p(v)=p(1)$

Work Step by Step

*NOTES TO REMEMBER: $f(x)$ is continuous at $a$ if and only if $$\lim\limits_{x\to a}f(x)=f(a)$$ We consider $\lim\limits_{v\to1}p(v)$ $=\lim\limits_{v\to1}2\sqrt{3v^2+1}$ $=2\sqrt{\lim\limits_{v\to1}(3v^2+1)}$ $=2\sqrt{3\lim\limits_{v\to1}v^2+\lim\limits_{v\to1}1}$ $=2\sqrt{3\times1^2+1}$ $=p(1)$ Therefore, $p(v)$ is continuous at $1$.
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