Single Variable Calculus

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Single Variable Calculus, Chapter 7, 7.7, Section 7.7, Problem 4

Expert Answers

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Determine the numerical value of a.) $\cos h 3$ and b.) $\cos h (\ln 3)$

a.) $\cos h 3$

Using Hyperbolic Function

$ \begin{equation} \begin{aligned} \cos h x =& \frac{e^x + e^{-x}}{2} \\ \\ \cos h 3 =& \frac{e^3 + e^{-3}}{2} \\ \\ \cos h 3 =& \frac{\displaystyle e^3 + \frac{1}{e^3}}{2} \\ \\ \cos h 3 =& \frac{e^6 + 1}{2e^3} \\ \\ \cos h 3 =& 10.067662 \end{aligned} \end{equation} $

b.) $\cos h (\ln 3)$

Using Hyperbolic Function

$ \begin{equation} \begin{aligned} \cos h x =& \frac{e^x + e^{-x}}{2} \\ \\ \cos h(\ln 3) =& \frac{e^{\ln 3} + e^{- \ln 3}}{2} \\ \\ \cos h(\ln 3) =& \frac{\displaystyle e^{\ln 3} + \frac{1}{e^{\ln 3}}}{2} \\ \\ \cos h(\ln 3) =& \frac{\displaystyle 3 + \frac{1}{3}}{2} \\ \\ \cos h(\ln 3) =& \frac{\displaystyle \frac{9 + 1}{3}}{2} \\ \\ \cos h(\ln 3) =& \frac{10}{2(3)} \\ \\ \cos h(\ln 3) =& \frac{10}{6} \\ \\ \cos h(\ln 3) =& \frac{5}{3} \end{aligned} \end{equation} $

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