Thread: solve limit with high powers

How do I calculate this limit?

Using L'Hospital's Rule... many times...

It is the only way?

No, you could also expand everything, then divide top and bottom by the highest power of .

The limit will be .

To see that notice that .

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.