I need some help to find this limit:

I tried to start doing something like

But then I don't know what to do with this and

Help?

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- Aug 8th 2010, 04:30 AMcrisLimits
I need some help to find this limit:

I tried to start doing something like

But then I don't know what to do with this and

Help? - Aug 8th 2010, 04:37 AMAlso sprach Zarathustra
Hint:

3^n < {2^n+3^n} < 2*3^n - Aug 8th 2010, 04:38 AMmr fantastic
- Aug 8th 2010, 04:39 AMPlato
- Aug 8th 2010, 05:45 AMcris
- Aug 8th 2010, 05:50 AMPlato
- Aug 8th 2010, 07:58 AMHallsofIvy
- Aug 8th 2010, 02:50 PMAlso sprach Zarathustra
3^n < {2^n+3^n} < 2*3^n

==>

{3^n}^{1/n} < {2^n+3^n}^{1/n} < {2*3^n}^{1/n}

==>

{3^n}^{1/n} < {2^n+3^n}^{1/n} < {2}^{1/n} * {3^n}^{1/n}

==>

3 < {2^n+3^n}^{1/n} < {2}^{1/n} * 3

==>

lim{3} <lim[ {2^n+3^n}^{1/n}] < lim[{2}^{1/n} * 3 ]

==>

3 <lim[ {2^n+3^n}^{1/n}] < 3 lim[{2}^{1/n} ]

{ lim 2^1/n =1 }

==>

3 <lim[ {2^n+3^n}^{1/n}] < 3

Applying sandwich rule :

lim[ {2^n+3^n}^{1/n}] = 3 - Aug 8th 2010, 04:28 PMPlato
What a mess that post is!

I am willing to bet that were Nietzsche alive today he would have embraced the use of LaTeX.

Why don’t you learn to use it? - Aug 8th 2010, 05:39 PMAllanCuz
Let

Wow. And after all that I end up at Mr. Fantastics result. I'm actually depressed.

In any event, to evaluate Mr. Fantastics limit we will revert one step.

Note how the 1 over n will tend towards 0 as n goes to infinity as will what is in the ln portion of the equation. We will end up with resulting in the answer 3. - Aug 8th 2010, 06:12 PMAlso sprach ZarathustraQuote:

What a mess that post is!

I am willing to bet that were Nietzsche alive today he would have embraced the use of LaTeX.

Why don’t you learn to use it?

Do you know who said:

Quote:

One man cannot practice many arts with success.