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

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SUMMARY

The discussion centers on evaluating the limit lim x->0 (1+x)^(1/x) and whether L'Hopital's Rule is necessary. Participants clarify that direct substitution leads to an indeterminate form, prompting the use of L'Hopital's Rule. The recommended approach involves taking the natural logarithm of the expression before applying L'Hopital's Rule to resolve the limit correctly. This method effectively simplifies the evaluation process.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hopital's Rule
  • Knowledge of natural logarithms
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the application of L'Hopital's Rule in various limit problems
  • Learn how to manipulate logarithmic expressions in calculus
  • Explore other techniques for evaluating indeterminate forms
  • Practice solving limits involving exponential functions
USEFUL FOR

Students studying calculus, particularly those grappling with limits and indeterminate forms, as well as educators looking for teaching strategies related to L'Hopital's Rule.

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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