Finding limit using l'Hopitals rule

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Homework Help Overview

The discussion revolves around finding the limit of the expression {e^(5+h)-e^5} / h as h approaches 0, utilizing l'Hôpital's rule. The subject area is calculus, specifically the application of limits and derivatives.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of l'Hôpital's rule, with one participant questioning their differentiation process and the resulting limit. Another participant seeks clarification on the rate of change of e^5 with respect to h, indicating a potential misunderstanding of constants in differentiation.

Discussion Status

The discussion is ongoing, with participants exploring the application of l'Hôpital's rule and questioning the correctness of the original poster's approach. There is an indication of productive dialogue as participants seek to clarify assumptions and reasoning.

Contextual Notes

There is a repeated emphasis on the nature of e^5 as a constant, which may be influencing the understanding of the limit and the application of differentiation in this context.

fran1942
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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'hospital's 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:
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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'hospital's 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'hospital's 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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