# How do you find the limit of #e^x/x^3# as x approaches infinity?

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To find the limit of e^x/x^3 as x approaches infinity, we can use L'Hôpital's rule. By applying this rule, we differentiate the numerator and denominator separately until we reach a determinate form.

Differentiating e^x with respect to x gives us e^x, and differentiating x^3 gives us 3x^2.

Taking the limit as x approaches infinity, we have e^x/3x^2.

Since the exponential function e^x grows faster than any polynomial, the limit of e^x/3x^2 as x approaches infinity is infinity.

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