# How do you find the limit of #(x ^ 3)(e ^ (-x ^ 2))# as x approaches infinity?

Write the limit as:

and again:

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To find the limit of (x^3)(e^(-x^2)) as x approaches infinity, we can use the concept of limits.

First, we can rewrite the expression as (x^3)/(e^(x^2)).

As x approaches infinity, the exponential function e^(x^2) grows much faster than any polynomial function, such as x^3.

Therefore, the exponential term dominates the expression, and the limit of (x^3)(e^(-x^2)) as x approaches infinity is 0.

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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.

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