# How do you find the limit of #[1/e^(x +1)]^sqrtx # as x approaches 0?

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To find the limit of [1/e^(x +1)]^sqrtx as x approaches 0, we can use the properties of limits and exponential functions.

First, let's simplify the expression.

[1/e^(x +1)]^sqrtx = e^(-sqrtx(x + 1))

Now, as x approaches 0, the term sqrtx approaches 0 as well.

Using the limit properties, we can rewrite the expression as:

e^(-sqrtx(x + 1)) = e^(-0(x + 1)) = e^0 = 1

Therefore, the limit of [1/e^(x +1)]^sqrtx as x approaches 0 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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