We were given the hint to try using the Squeeze Theorem in order to find the(adsbygoogle = window.adsbygoogle || []).push({});

limit as n → ∞ of the sequence {(2^n + 3^n)^(1/n)}.

I understand the concept of the squeeze theorem that I need to find functions A and B such that A ≤ {(2^n + 3^n)^(1/n)} ≤ B, and A and B limit to the same quantity, say "L."

So lim A = lim B = L, so that I can conclude that lim (2^n + 3^n)^(1/n) = L.

I don't know how to come up with those functions. It has been 2 years since I last took a calculus class, so I am very rusty with limits.

So far all I have is that 0 ≤ {(2^n + 3^n)^(1/n)} ≤ 2^n + 3^n.

So I can say 0 limits to 0, but then how would I evaluate

the limit of 2^n + 3^n as n approaches ∞? It would just keep getting bigger so I would have that limit as ∞. So I am stuck with 0 and ∞ as limits which is wrong because A and B are supposed to limit to the same value.

Any help, tips, corrections, and/or suggestions is greatly appreciated.

Thank you for your time!

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# Homework Help: Help with using the Squeeze Theorem to find a limit.

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