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AlexFokin [52]
3 years ago
13

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh(9) (b) cosh(ln(9))

Mathematics
1 answer:
hoa [83]3 years ago
5 0

Answer:

a) \cosh 9 \approx 4051.54203, b) \cosh (\ln 9) \approx 4.55556.

Step-by-step explanation:

a) As we remember, hyperbolic cosine is represented by the following expression:

\cosh x = \frac{e^{x}+e^{-x}}{2}

\cosh x = \left(\frac{1}{2\cdot e^{x}}\right) \cdot (e^{2\cdot x}+1)

The numerical value of \cosh 9 is:

\cosh 9 = \left(\frac{1}{2\cdot e^{9}} \right)\cdot (e^{18}+1)

\cosh 9 \approx 4051.54203

b) By using the definition presented and developed in item a), we get the following expression:

\cosh x = \left(\frac{1}{2\cdot e^{\ln 9}}\right) \cdot (e^{2\cdot \ln 9}+1)

Now, we simplify this by using power and logarithm properties:

\cosh (\ln 9) = \left[\frac{1}{(2)\cdot (9)} \right]\cdot (9^{2}+1)

\cosh (\ln 9) = \frac{82}{18}

\cosh (\ln 9) = \frac{41}{9}

\cosh (\ln 9) \approx 4.55556

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