Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.11 - Hyperbolic Functions - 3.11 Exercises - Page 264: 2


a) $$0$$ b) $$\frac{e^2-1}{e^2+1}$$

Work Step by Step

To solve part a and b of this question, it is important to know that: $\tanh = \frac{\sinh x}{\cosh x} =\frac{\frac{e^x-e^{-x}}{2}}{\frac{e^x+e^{-x}}{2}} =\frac{e^x-e^{-x}}{e^x+e^{-x}}$ a) $\tanh 0$ $=\frac{e^0-e^{-0}}{e^0+e^{-0}}=\frac{1-1}{1+1}=\frac{0}{2}=0$ b) $\tanh1$ $=\frac{e^1-e^{-1}}{e^1+e^{-1}}=\frac{e-\frac{1}{e}}{e+\frac{1}{e}} =\frac{e^2-1}{e^2+1}$
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