If `f(n)=lim_(xto0) {(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"sin"(x)/(2^(n)))}^((1)/(x))` then find `lim_(ntooo) f(n).`

Explanation

To solve the problem, we need to find the limit of the function \( f(n) \) as \( n \) approaches infinity, where:

\[ f(n) = \lim_{x \to 0} \left( \left(1 + \frac{\sin x}{2}\right) \left(1 + \frac{\sin x}{2^2}\right) \cdots \left(1 + \frac{\sin x}{2^n}\right) \right)^{\frac{1}{x}} \]

### Step-by-Step Solution:

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