e^(-1/2) - e^(-1/4)
You asked:
Evaluate the expression: \({e}^{\frac{-1}{2}} - {e}^{\frac{-1}{4}}\)
MathBot Answer:
\[{e}^{\frac{-1}{2}} - {e}^{\frac{-1}{4}} = - \frac{1}{e^{\frac{1}{4}}} + e^{- \frac{1}{2}} \approx -0.17227012335877144464137073198714\]
\[\begin{aligned}{e}^{\frac{-1}{2}} - {e}^{\frac{-1}{4}}& = \frac{1}{\sqrt{e}} - \frac{1}{\sqrt[4]{e}}\\& = e^{- \frac{1}{2}} - \frac{1}{\sqrt[4]{e}}\\& = e^{- \frac{1}{2}} - e^{- \frac{1}{4}}\\& = - e^{- \frac{1}{4}} + e^{- \frac{1}{2}}\end{aligned}\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).