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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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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