What is the limit as x approaches 0 of (e^{-1/x})^x ?

The limit as x approaches 0 of (e^{-1/x})^x is 1/e

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limit as x approaches 0 of (e^{-1/x})^x

x \to 0 lim ((e^{- \frac{1}{x}})^{x})

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

x \to 0 lim ((e^{- \frac{1}{x}})^{x})

(e^{- \frac{1}{x}})^{x} = \frac{1}{e}

= x \to 0 lim (\frac{1}{e})

x \to a lim c = c

= \frac{1}{e}

What is the limit as x approaches 0 of (e^{-1/x})^x ?
The limit as x approaches 0 of (e^{-1/x})^x is 1/e