Mathematics

Problem

f(x)=\lim_{n\rightarrow \infty}\sin^{2n}(\pi x)+\left[x+\frac{1}{2}\right]

, where

[\cdot]

denotes the greatest integer function, is (a) continuous at

x=1

, but discontinuous at

x=3/2

(b) continuous at

x=1

and

x=3/2

x=1

and

x=3/2

(d) discontinuous at

x=1

but continuous at

x=3/2