5/4 ⋅(e^4−e^−4)

asked by guest
on Nov 22, 2024 at 7:48 pm



You asked:

Evaluate the expression: \(\frac{5}{4} \cdot \left({e}^{4} - {e}^{-4}\right)\)

MathBot Answer:

\[\frac{5}{4} \cdot \left({e}^{4} - {e}^{-4}\right) = - \frac{5}{4 e^{4}} + \frac{5 e^{4}}{4} \approx 68.22479299281938112227067897698455\]


\[\begin{aligned}\frac{5}{4} \cdot \left({e}^{4} - {e}^{-4}\right)& = \frac{5}{4} \cdot \left(e^{4} - \frac{1}{e^{4}}\right)\\& = \frac{5}{4} \cdot \left(e^{4} - e^{-4}\right)\\& = \frac{5}{4} \cdot \left(- e^{-4} + e^{4}\right)\\& = - \frac{5}{4} \cdot e^{-4} + \frac{5}{4} \cdot e^{4}\end{aligned}\]


\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).