# Finding limit using l'Hopitals rule

• fran1942
In summary, the conversation discusses using l'Hopital's rule to solve a limit involving e^(5+h) and e^5. The individual attempts to differentiate both numerator and denominator and obtains a limit of 0, but believes the limit should actually be e^5. They ask for help in understanding where they went wrong.
fran1942
Hello, I am tying to use l'Hopital's rule to solve this limit:
{e^(5+h)-e^5} / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly

Last edited:
fran1942 said:
Hello, I am tying to use l'Hopital's rule to solve this limit:
e^(5+h)-e^5 / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly
What is the rate of change of e^5 with respect to h? I am assuming you are dealing with { e(5+h) - e^5 }/h.

Last edited:
RoshanBBQ said:
What is the rate of change of e^5 with respect to h? I am assuming you are dealing with { e(5+h) - e^5 }/h.

yes, that is correct. I am trying to apply l'Hopital's rule to that formula to obtain the limit as h tends towards 0.
I don't think I have it right in my attempt above. Any help would be appreciated.

Thank you.

fran1942 said:
Hello, I am tying to use l'Hopital's rule to solve this limit:
{e^(5+h)-e^5} / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly

e^5 is a constant. What's the derivative of a constant?

## What is l'Hopital's rule and how does it work?

L'Hopital's rule is a mathematical technique used to evaluate the limit of a function at a specific point, when the limit cannot be easily determined using algebra. It states that if the limit of a fraction of two functions is of the form 0/0 or ∞/∞, then the limit can be found by taking the derivative of the numerator and denominator separately and then evaluating the limit again.

## When can l'Hopital's rule be applied?

L'Hopital's rule can only be applied when the limit of a fraction of two functions is of the form 0/0 or ∞/∞. If the limit is not in this form, then the rule cannot be used and other techniques must be employed to find the limit.

## What are the steps to using l'Hopital's rule?

The steps to using l'Hopital's rule are as follows:

1. Identify the limit you want to evaluate.
2. Check if the limit is in the form 0/0 or ∞/∞.
3. If the limit is in this form, take the derivative of the numerator and denominator separately.
4. Evaluate the limit again using the new derivatives.
5. If the limit is still in the form 0/0 or ∞/∞, repeat the process until the limit can be evaluated.

## Are there any limitations to using l'Hopital's rule?

Yes, there are limitations to using l'Hopital's rule. It can only be applied to indeterminate forms of 0/0 or ∞/∞, and it may not always give the correct answer. It is important to check other methods of finding the limit if l'Hopital's rule does not work or gives a different answer.

## Can l'Hopital's rule be used for any type of function?

No, l'Hopital's rule can only be used for functions that are differentiable, meaning their derivatives exist and are continuous. It cannot be used for functions with discontinuities or vertical asymptotes.

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