Limit Question (Using logarithm and L'Hopital's Rule)

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SUMMARY

The discussion focuses on solving a limit problem using logarithmic properties and L'Hopital's Rule. Participants clarify that ln(a/b) equals ln(a) - ln(b) and emphasize the importance of manipulating the limit expression correctly. The conversation highlights the need to apply the definition of e and the laws for manipulating limits to arrive at the solution. Suggestions include moving the limit around in the original expression to simplify the problem.

PREREQUISITES
  • Understanding of logarithmic properties, specifically ln(a/b) = ln(a) - ln(b)
  • Familiarity with L'Hopital's Rule for evaluating indeterminate forms
  • Knowledge of limits and their manipulation techniques
  • Basic understanding of the mathematical constant e and its definition
NEXT STEPS
  • Study the application of L'Hopital's Rule in various limit problems
  • Learn advanced logarithmic identities and their applications in calculus
  • Explore the definition and properties of the constant e in calculus
  • Practice manipulating limits through various algebraic techniques
USEFUL FOR

Students studying calculus, particularly those tackling limit problems, as well as educators looking for examples of limit manipulation techniques using logarithms and L'Hopital's Rule.

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Note that ln(a/b) != ln a/ln b
 
Last edited by a moderator:
You're going about it completely the wrong way. Try moving the limit around in the original expression.
 
I apologize but what do you mean and how? Can you show some steps it's been a while and due date is coming up soon and I still haven't figured it out!
 
neden said:
I apologize but what do you mean and how? Can you show some steps it's been a while and due date is coming up soon and I still haven't figured it out!

Remember that:

e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n

by definition. Also remember the laws for manipulating limits.
 

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