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

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To find the limit of (1/x)^x as x approaches infinity, we can rewrite the expression as e^(x * ln(1/x)). Using the property that ln(a/b) = ln(a) - ln(b), we can simplify it further to e^(x * (ln(1) - ln(x))). Since ln(1) is equal to 0, the expression becomes e^(-x * ln(x)). As x approaches infinity, ln(x) also approaches infinity. Therefore, the limit of (1/x)^x as x approaches infinity is 0.

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The limit of ( \left(\frac{1}{x}\right)^x ) 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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