If `f(x)=(tanx)/(x)`, then find `lim_(xto0)([f(x)]+x^(2))^((1)/([f(x)]))`, where `[.]` and `{.}` denotes greatest integer and fractional part function respectively.

Explanation

To solve the limit \( \lim_{x \to 0} \left( [f(x)] + x^2 \right)^{\frac{1}{\{f(x)\}}} \), where \( f(x) = \frac{\tan x}{x} \), we will follow these steps:

### Step 1: Evaluate \( f(x) \) as \( x \to 0 \)

We know that:
\[ f(x) = \frac{\tan x}{x} \]
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