evaluate the following expression. round your answer to two decimal places. if the value does not exist…

Explanation:

Step1: Recall the definition of hyperbolic sine function

The hyperbolic sine function is defined as $\sinh x=\frac{e^{x}-e^{-x}}{2}$.

Step2: Substitute (x = 2) into the formula

When (x = 2), we have $\sinh2=\frac{e^{2}-e^{-2}}{2}$. We know that (e^{2}\approx7.389056) and (e^{-2}=\frac{1}{e^{2}}\approx0.135335). Then (e^{2}-e^{-2}\approx7.389056 - 0.135335=7.253721).

Step3: Calculate the value of (\sinh2)

(\sinh2=\frac{7.253721}{2}=3.6268605).

Answer:

(3.63)