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## Homework Statement

lim of (a^x-a^-x-2)/(x^2) as x->0

Find the value of the limit^.

The answer is (lna)^2

I know how to get the answer using L'Hospital.

However, I do not want to use Hospital's rule.

I think I see the pattern with the special limit:

lim of (e^x-1)/x as x->0

But I just don't see how I can apply that. I tried to take ln() out of everything, but it leads me to nowhere.

Please help me.