Question

evaluate the following expression. round your answer to two decimal places. if the value does not exist, write dne for your answer. sinh2

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:

\(3.63\)