How do I calculate this limit? http://i51.tinypic.com/2nvs5lu.png

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- Nov 6th 2010, 02:01 AMdrugcppsolve limit with high powers
How do I calculate this limit? http://i51.tinypic.com/2nvs5lu.png

- Nov 6th 2010, 02:13 AMProve It
Using L'Hospital's Rule... many times...

- Nov 6th 2010, 02:47 AMdrugcpp
It is the only way?

- Nov 6th 2010, 02:53 AMProve It
No, you could also expand everything, then divide top and bottom by the highest power of $\displaystyle x$.

- Nov 6th 2010, 04:28 AMPlato
The limit will be $\displaystyle \left(\frac{3}{2}\right)^{20}$.

To see that notice that $\displaystyle (3x-1)^{20}=3^{20}x^{20}\left(1-\frac{1}{3x}\right)^{20}$. - Nov 6th 2010, 05:16 AMdrugcpp
I did it in a different, longer way.

(3x-1)^20 = ((3x-1)²)^10.

This way I've put the power of ten outside the whole expression and after a couple of lines ended up with (9/4)^10.

Your way is much shorter, I should notice such things in the future, thanks.