# What is the limit of x/e^x as x approaches infinity?

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#### Explanation

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#### Explanation:

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20
Jul 19, 2016

lim_(x->∞) x/e^x = 0

#### Explanation:

Since direct substitution yields an indeterminate form of ∞/∞, we can conclude that we can apply L'Hospital's rule, which basically involves taking a derivative of the numerator and the denominator.

In our case, we have

lim_(x->∞) x/e^x = lim_(x->∞) 1/e^x = 0

This makes sense because if we look at the graph of the original function, we can see that the function clearly approaches $0$ as x->∞.

graph{x/e^x [-1.856, 5.072, -1.588, 1.877]}

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