How Can You Use a Fact to Evaluate Limits?

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SUMMARY

This discussion focuses on evaluating limits using specific mathematical facts rather than traditional methods like L'Hôpital's Rule. The limit in question is expressed as lim_{n→∞} (n+4)/(n-4)^n, which simplifies to (n+4)/(n-4)^n as n approaches infinity. The correct approach involves substituting 1/x for n and evaluating the limit as x→0^+. This method provides a clear alternative to standard limit evaluation techniques.

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islandboy401
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Using a fact to find a limit??

If I were given a problem to find this limit:

limit%20calc.JPG


using the fact that

limit%20calcs.JPG


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."
 
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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.
 

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