# How do you find the limit of #(x/(x+1))^x# as x approaches #oo#?

The limit is

we can write this as

Hence actually we need to find the limit

Because

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To find the limit of (x/(x+1))^x as x approaches infinity, we can use the concept of exponential limits.

First, we rewrite the expression as (1 + 1/x)^(-x).

Next, we take the limit as x approaches infinity.

Using the limit property, we have e^(-1) as the limit, where e is the base of the natural logarithm.

Therefore, the limit of (x/(x+1))^x as x approaches infinity is e^(-1).

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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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