# finding limit using l'Hopitals rule

by fran1942
Tags: lhopitals, limit, rule
 P: 80 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
P: 281
 Quote by 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
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.
P: 80
 Quote by RoshanBBQ 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 dont think I have it right in my attempt above. Any help would be appreciated.

Thank you.

HW Helper
P: 2,644

## finding limit using l'Hopitals rule

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

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