How Can You Use a Fact to Evaluate Limits?

[islandboy401]

Using a fact to find a limit??

If I were given a problem to find this limit:

using the fact that

how would I do it?

I know how to evaluate this limit using L'Hopital's Rule...but I am not to sure on evaluating using this "fact."

 

[Citan Uzuki]

Well, since x is not a variable in \left(\frac{n+4}{n-4}\right)^n, we have:

\lim_{x\rightarrow \infty} \left(\frac{n+4}{n-4}\right)^n = \left(\frac{n+4}{n-4}\right)^n.

Assuming you meant \lim_{n\rightarrow\infty}, start by substituting 1/x for n in the function, and take the limit of the result as x\rightarrow0^+.

P.S. this belongs in homework help.