What is the Limit of (E^x+1)^1/x as x Approaches Infinity?

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (E^x - 1)^(1/x) as x approaches infinity. The subject area includes limits and exponential functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential use of L'Hôpital's rule and the application of logarithms to simplify the limit. There are questions about the correct approach to applying the natural logarithm to the limit expression.

Discussion Status

Some participants have offered guidance on using logarithms and L'Hôpital's rule, while others express uncertainty about the application of these methods. Multiple interpretations of the limit's evaluation are being explored.

Contextual Notes

There is a mention of the need to show work when applying L'Hôpital's rule, indicating a focus on the process of solving the limit rather than just the outcome.

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Homework Statement



Lim (E^x-1)^(1/x)
x->Infinito

L'Hospital?

Homework Equations



Lim (1+1/x)^x=E
x->Infinito

The Attempt at a Solution



Help!
 
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If you want to use l'Hopital you will have to take the logarithm of the limit first. Remember [itex]e^{\ln x} =x[/itex] and don't forget to show us your work!
 
Last edited:
Thank you very much for your advice.

I'm still unsure how to approach this one. Apply Ln() to the entire limit?
 
Yes write the limit as [itex]\exp(\ln[(e^x-1)^{(1/x)}])[/itex].
 

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