- #1
Chipset3600
- 79
- 0
Hello MHB, how can i solve this limit without L'Hospital rule?
Here is a litle bit of my solution:
Here is a litle bit of my solution:
Chipset3600 said:Hello MHB, how can i solve this limit without L'Hospital rule?
Here is a litle bit of my solution:
Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...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$\chi$ $\sigma$
Chipset3600 said:Oh yeah! I forgot the fundamental limit :s, so is =2ln(10)...
Thanks
A limit is the value that a function or sequence approaches as the input or index approaches a certain value or infinity.
One method is to use algebraic manipulation and simplification to rewrite the function in a form that allows for direct substitution of the limiting value. Another method is to use the properties of limits, such as the sum, difference, product, and quotient rules.
The most common indeterminate forms are 0/0, ∞/∞, 0∙∞, and ∞-∞.
L'Hospital's rule can only be used when the limit is in an indeterminate form of 0/0 or ∞/∞.
L'Hospital's rule can only be used for certain types of limits and it may not always give the correct result. It also does not work for limits involving discontinuous functions or limits at infinity.