Evaluate `lim_(xtooo) 2^(x-1)tan((a)/(2^(x))).`

Explanation

To evaluate the limit \( \lim_{x \to \infty} 2^{(x-1)} \tan\left(\frac{a}{2^x}\right) \), we will follow a step-by-step approach.

### Step 1: Analyze the limit
As \( x \) approaches infinity, \( 2^x \) approaches infinity. Thus, \( \frac{a}{2^x} \) approaches 0. Therefore, we can rewrite the limit as:
\[ \lim_{x \to \infty} 2^{(x-1)} \tan\left(\frac{a}{2^x}\right) \]

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