# How do you find the limit of #(1-(2/x))^x# as x approaches infinity?

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To find the limit of (1-(2/x))^x as x approaches infinity, we can use the concept of exponential limits.

First, we rewrite the expression as (1-(2/x))^(x/x).

Next, we take the limit as x approaches infinity.

Using the limit properties, we have (1^∞), which is an indeterminate form.

To evaluate this, we can rewrite it as e^(ln(1-(2/x))^x).

Now, we can rewrite ln(1-(2/x))^x as x * ln(1-(2/x)).

Taking the limit as x approaches infinity, we have x * ln(1-(2/x)) = x * (-2/x) = -2.

Finally, we have e^(-2) as the limit of (1-(2/x))^x as x approaches infinity.

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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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