Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Exercises: 10

Answer

$$\lim\limits_{v\to4^+}\frac{4-v}{|4-v|}=-1$$

Work Step by Step

$$A=\lim\limits_{v\to4^+}\frac{4-v}{|4-v|}$$ We see that $|4-v|=(4-v)$ if $(4-v)\ge0$ or $v\le4$ and $|4-v|=-(4-v)$ if $(4-v)\lt0$ or $v\gt4$ In this case, since $v\to4^+$, we only consider the values of $v\gt4$. Therefore, $|4-v|=-(4-v)$ So, $$A=\lim\limits_{v\to4^+}\frac{4-v}{-(4-v)}$$$$A=\lim\limits_{v\to4^+}\frac{1}{-1}$$$$A=\lim\limits_{v\to4^+}(-1)$$$$A=-1$$
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