# Limit, without L'hospital rule

#### Chipset3600

##### Member
Hello MHB, how can i solve this limit without L'Hospital rule?
Here is a litle bit of my solution:

#### chisigma

##### Well-known member
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

##### Member
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

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...
Thanks
Evaluate it using L'Hospital rule and verify your result .