evaluate the function. if the value is not a rational number, round your answer to three decimal…

Explanation:

Step1: Recall the definition of cosh x

The hyperbolic - cosine function is defined as $\cosh x=\frac{e^{x}+e^{-x}}{2}$. When $x = 0$, we substitute $x = 0$ into the formula. $\cosh(0)=\frac{e^{0}+e^{-0}}{2}$ Since $e^{0}=1$ and $e^{-0}=1$, then $\cosh(0)=\frac{1 + 1}{2}=1$.

Step2: Recall the definition of sech x

The hyperbolic - secant function is defined as $\text{sech}x=\frac{1}{\cosh x}=\frac{2}{e^{x}+e^{-x}}$. When $x = 3$, we substitute $x = 3$ into the formula. $\text{sech}(3)=\frac{2}{e^{3}+e^{-3}}$ We know that $e^{3}\approx20.086$ and $e^{-3}=\frac{1}{e^{3}}\approx0.0498$. Then $e^{3}+e^{-3}\approx20.086 + 0.0498=20.136$. So $\text{sech}(3)=\frac{2}{20.136}\approx0.099$.

Answer:

(a) 1 (b) 0.099