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

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

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

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

\infty

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

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

Apply the Limit Chain Rule:

\infty

= \infty

x \to 1 lim (1 - \frac{1}{x})

x \to 0 lim (\frac{5 x}{3 x})

x \to 0 lim ((x + 3) (x^{2} - 4))

x \to 0 lim (csc (3 x))

x \to 15 lim (\frac{1}{x - 15})

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