# How do you determine the limit of #n^n/(n!)# as n approaches infinity?

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To determine the limit of n^n/(n!) as n approaches infinity, we can use the concept of the ratio test. By applying the ratio test, we can simplify the expression and evaluate the limit.

First, let's rewrite the expression as (n/n) * (n/n-1) * (n/n-2) * ... * (n/2) * (n/1).

Next, we can simplify each term by canceling out common factors. This results in n * (1/n-1) * (1/n-2) * ... * (1/2) * (1/1).

Now, we can observe that as n approaches infinity, each term in the expression (1/n-1), (1/n-2), ..., (1/2), (1/1) approaches zero.

Therefore, the limit of n^n/(n!) as n approaches infinity is zero.

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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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