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

[Chipset3600]

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

 

[chisigma]

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$\chi$ $\sigma$

 

[Chipset3600]

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

 

[alyafey22]

Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...
Thanks

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