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

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The discussion focuses on solving a limit without using L'Hospital's Rule. Participants emphasize the importance of using fundamental limits for a more rigorous approach, specifically referencing the limit that leads to Euler's number, e. One user acknowledges forgetting the fundamental limit and corrects their solution to 2ln(10). There is a suggestion to evaluate the limit using L'Hospital's Rule for verification. The conversation highlights different methods for approaching limit problems in calculus.
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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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