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

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To find the limit of (x/(x+1))^x as x approaches infinity, we can rewrite the expression using the natural logarithm. Taking the natural logarithm of both sides, we have ln((x/(x+1))^x). Using the properties of logarithms, we can simplify this expression to x ln(x/(x+1)).

Next, we can use the limit properties to evaluate the limit. As x approaches infinity, ln(x/(x+1)) approaches ln(1) which is 0. Therefore, the limit of x ln(x/(x+1)) as x approaches infinity is 0.

Hence, the limit of (x/(x+1))^x as x approaches infinity is 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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