Find the limit of $\frac{e^{-x}}{x}$ as $x$ approaches $\infty $

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

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

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

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Learn how to solve limits to infinity problems step by step online. Find the limit of (e^(-x))/x as x approaches infinity. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Evaluate the limit \lim_{x\to\infty }\left(\frac{1}{xe^x}\right) by replacing all occurrences of x by \infty . Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value e. If you multiply a very large number by another very large number, you get an even bigger number, so infinity times infinity equals infinity: \infty\cdot\infty=\infty.

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Function Plot

Plotting: $\frac{e^{-x}}{x}$

Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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