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

  • MHB
  • Thread starter Chipset3600
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In summary, the conversation is about solving a limit without using L'Hospital's rule and instead relying on the fundamental limits. The final result is 2ln(10). The use of fundamental limits is considered to be more rigorous than l'Hopital's rule or Taylor expansion. The speaker also mentions the use of the fundamental limit $\displaystyle \lim_{n \rightarrow \infty} (1 + \frac{1}{n})^{n} = e$, which is helpful in solving the limit. Finally, the speaker suggests verifying the result using L'Hospital's rule.
  • #1
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:
 
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  • #2
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$\chi$ $\sigma$
 
  • #3
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
 
  • #4
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 .
 

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

What is a limit?

A limit is the value that a function or sequence approaches as the input or index approaches a certain value or infinity.

How do you find a limit without L'Hospital's rule?

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.

What are the common types of indeterminate forms?

The most common indeterminate forms are 0/0, ∞/∞, 0∙∞, and ∞-∞.

When can you use L'Hospital's rule?

L'Hospital's rule can only be used when the limit is in an indeterminate form of 0/0 or ∞/∞.

What are the limitations of L'Hospital's rule?

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.

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