The function \(f(z)=\frac{(z-1)}{(z-2)}\sin \frac{1}{z-\frac{1}{2}}\) has
1
A zero at z = 1 of order one and isolated essential singularity at \(z=\frac{1}{2}\)
2
A zero at z = 2 of order one and isolated essential singularity at \(z=\frac{1}{2}\)
3
A simple pole at z = 2 and non-isolated essential singularity at \(z=\frac{1}{2}\)
4
A double pole at z = 1 and isolated essential singularity at \(z=\frac{1}{2}\)