Question

Which of the following function is continuous (where [.] denotes the greatest integer function)

• A. $\cos \left[x\right]$
• B. $\sin \pi \left[x\right]$
• C. $\cos \frac{\pi }{2}\left[x\right]$
• D. both b and c

Answer 1

The correct option is B $\sin \pi \left[x\right]$

We know that $\left[x\right]$ will only give integer values and $\sin \pi \left[x\right]$ will give $0$.
Hence, $\sin \pi \left[x\right]$ will only be continuous.