Solving Homework Problem: ln and e Inverse Process

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SUMMARY

The discussion focuses on solving a homework problem involving the natural logarithm and the exponential function, specifically the limit of ln(y) as n approaches infinity. The user correctly identifies that the limit leads to an indeterminate form of 0 times infinity and seeks clarification on applying L'Hôpital's Rule to resolve it. The solution ultimately confirms that the limit evaluates to e, demonstrating the inverse relationship between ln and e.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hôpital's Rule
  • Knowledge of natural logarithms and exponential functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the application of L'Hôpital's Rule in various limit problems
  • Study the properties of logarithmic and exponential functions
  • Practice solving limits involving indeterminate forms
  • Explore advanced calculus topics related to continuity and differentiability
USEFUL FOR

Students studying calculus, particularly those tackling limits and the properties of logarithmic and exponential functions, as well as educators looking to reinforce these concepts in their teaching.

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Homework Statement



http://img513.imageshack.us/img513/2687/problem15001.jpg

Homework Equations



I know the answer is e but i forgat how to do the lny=xln(1+1/n) and then I solve an get an e because ln and e are inverse but i forgot the process can you please show me the process

The Attempt at a Solution

 
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at the stage

\stackrel{lim}{n \rightarrow \infty}, ln(y) = n.ln(1+1/n)

the limit is indeterminant 0 * infinity, so can you re-write it and use l'hospital's rule...?
 

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