Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.7 Hyperbolic Functions - 6.7 Exercises - Page 489: 4


a) $\dfrac{e^8-1}{2e^4}$; b) $\dfrac{15}{8}$

Work Step by Step

Apply definition of hyperbolic function for $\sinh x$ a) $\sinh 4=\dfrac{e^4-e^{-4}}{2}$ or, $=\dfrac{e^4-\frac{1}{e^4}}{2}$ or, $=\dfrac{\frac{e^8-1}{e^4}}{2}$ or, $=\dfrac{e^8-1}{2e^4}$ b) $\sinh ({\ln4})=\dfrac{e^{\ln 4}-e^{-({\ln 4})}}{2}$ or, $=\dfrac{4-\dfrac{1}{4}}{2}$ or, $=\dfrac{\dfrac{15}{4}}{2}$ or, $=\dfrac{15}{8}$
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