Find Limit, as x goes to 0, of [2^(2x) - 2^x]/[2^x - 1]

[K_Swiss]

Evaluate.

Textbook Answer: 16

Please show me in steps on how to solve this equation

 

[pka]

Re: Finding the Limit

That given answer is incorrect. The limit is 1.
\(\displaystyle \left( {2^x } \right)\left( {2^x } \right) = 2^{2x} \quad \Rightarrow \quad 2^{2x} - 2^x = 2^x (2^x - 1)\).