How do you evaluate the limit $\frac{e^{- x}}{x}$ $e^(-x)/x$ as x approaches $\infty$ $oo$ ?

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How do you evaluate the limit $\frac{e^{- x}}{x}$ $e^(-x)/x$ as x approaches $\infty$ $oo$ ?

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Answer 1 · 2016-12-25T04:02:35

$lim_(x->oo)e^(-x)/x = 0$

Explanation:

To calculate this limit, we just recall that $a^(-b) = 1/a^b$ and note that $lim_(x->oo)e^x=oo$ and $lim_(x->oo)x = oo$ , meaning $lim_(x->oo)xe^x = oo$ . With those, we have

$lim_(x->oo)e^(-x)/x = lim_(x->oo)1/(xe^x) = 1/oo = 0$

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How do you evaluate the limit $\frac{e^{- x}}{x}$ $e^(-x)/x$ as x approaches $\infty$ $oo$ ?

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How do you evaluate the limit $\frac{e^{- x}}{x}$ $e^(-x)/x$ as x approaches $\infty$ $oo$ ?