If \(f(x)=\begin{cases} \ln x & \text{for } 0\lt x \leq 2 \\ x^2\ln 2 & \text{for } 2\lt x\leq 4 \end{cases} \) , then \(\lim\limits_{x\to 2}f(x) \) is

Find the left and right hand limits.

Since the left and right hand limits do not equal each other, the limit is nonexistent.