How Can I Solve This Limit Without L'Hospital's Rule?

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Discussion Overview

The discussion revolves around solving a limit problem without using L'Hospital's Rule. Participants explore alternative methods, including the application of fundamental limits and Taylor expansion, while sharing their partial solutions and reasoning.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant asks how to solve a limit without L'Hospital's Rule and shares part of their solution.
  • Another participant suggests that while L'Hospital's Rule or Taylor expansion may be more convenient, using fundamental limits is considered more rigorous.
  • A later reply acknowledges the importance of the fundamental limit and provides a specific result related to the limit being discussed.
  • One participant suggests evaluating the limit using L'Hospital's Rule to verify the result.

Areas of Agreement / Disagreement

Participants express differing views on the methods used to solve the limit, with some favoring fundamental limits for rigor while others suggest more comfortable methods like L'Hospital's Rule or Taylor expansion. The discussion remains unresolved regarding the preferred approach.

Contextual Notes

There are missing assumptions regarding the specific limit being discussed, and the dependence on definitions of fundamental limits and Taylor expansion is not fully explored. The mathematical steps leading to the conclusions are not detailed.

Chipset3600
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Hello MHB, how can i solve this limit without L'Hospital rule?
Here is a litle bit of my solution:
http://i.imgur.com/aEpCDY7.jpg
 
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Chipset3600 said:
Hello MHB, how can i solve this limit without L'Hospital rule?
Here is a litle bit of my solution:

Excellent!... of course l'Hopital's rule or Taylor expansion is more comfortable but the use of the 'fundamental limits' [in Your case $\displaystyle \lim_{n \rightarrow \infty} (1 + \frac{1}{n})^{n} = e$...] is allwais more 'rigorous'...

Kind regards$\chi$ $\sigma$
 
chisigma said:
Excellent!... of course l'Hopital's rule or Taylor expansion is more comfortable but the use of the 'fundamental limits' [in Your case $\displaystyle \lim_{n \rightarrow \infty} (1 + \frac{1}{n})^{n} = e$...] is allwais more 'rigorous'...

Kind regards$\chi$ $\sigma$
Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...
Thanks
 
Chipset3600 said:
Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...
Thanks

Evaluate it using L'Hospital rule and verify your result .
 

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