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

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To find the limit of (e^x + sin(x) + x - 1)/(e^x - 1) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (e^x + cos(x) + 1)/(e^x). Evaluating this expression at x = 0, we have (1 + 1 + 1)/(1) = 3. Therefore, the limit of the given expression as x approaches 0 is 3.

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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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