A function `f(x)` defined in the domain `0 \le x \le 3` by following.
$f(x)=\begin{cases} 2x-3,& \text{when } 0 \le x \le 2\\ x^2, & \text{when } x=2 \\\frac{x}{2}, & \text{when }2 \le x \le 3 \end{cases}$
Find the value of `lim_{x \to 2} f(x)` if exists.