Do I even need to use L'Hopital's Rule for this

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (1+x)^(1/x) as x approaches 0, with a focus on whether L'Hopital's Rule is necessary for the evaluation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of directly substituting x=0 into the limit and question the implications of undefined expressions. There is mention of using L'Hopital's Rule and taking the logarithm of the expression as a potential approach.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the limit and the appropriateness of applying L'Hopital's Rule. Some guidance has been offered regarding the use of logarithms and L'Hopital's Rule, but no consensus has been reached.

Contextual Notes

There is a mention of confusion regarding the substitution of zero and the nature of the limit, indicating a need for clarification on these points.

tjohn101
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Homework Statement


Evaluate the limit analytically if necessary using L’Hopital’s rule:
lim x->0 (1+x)1/x


Homework Equations





The Attempt at a Solution


Well, I can get the thing equal to 1 if I just plug in zero, so do I need to use L'hopital's? This whole thing is very confusing...
 
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How can you 'plug in 0'?? 1/0 is undefined. Besides the limit isn't 1. I suggest you use l'Hopital.
 
To be honest, it's late and I've been doing this stuff for 9 hours straight. It didn't even cross my mind that 1/0 would be undefined.
 
Gotcha. So just take the log and use l'Hopital on the result.
 

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