Find the limit of (e^(-x))/x as x approaches -infinity

 Exercise

$\lim_{x\to-\infty}\left(\frac{e^{-x}}{x}\right)$

 

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\lim_{x\to{- \infty }}\left(\frac{1}{xe^x}\right)$

 

Evaluate the limit $\lim_{x\to{- \infty }}\left(\frac{1}{xe^x}\right)$ by replacing all occurrences of $x$ by $- \infty $

$\frac{1}{- \infty \cdot e^{- \infty }}$

 

Apply the formula: $n^{- \infty }$$=0$, where $n=e$

$\frac{1}{0}$

 

An expression divided by zero tends to infinity

$\infty $

$\infty $

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