# Given #((e^h)-1)/(h)# how do you find the limit as h approaches 0?

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I may be wrong but I think we should still be allowed to use Bernoulli's compounding formula

So

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To find the limit as h approaches 0 for the expression ((e^h)-1)/(h), we can use L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately and then evaluate the limit again.

Differentiating the numerator, we get e^h. Differentiating the denominator, we get 1.

Now, we can evaluate the limit again by substituting h = 0 into the differentiated expression:

lim(h→0) (e^h)/(1)

Simplifying further, we have:

lim(h→0) e^h

Finally, substituting h = 0 into the expression, we get:

lim(h→0) e^0 = e^0 = 1

Therefore, the limit as h approaches 0 for ((e^h)-1)/(h) is equal to 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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