Question

If $f\left(x\right)=\sin \pi \left[x\right]$, where $[\cdot ]$ denotes greatest integer function, then $f^{{}^{\prime }}\left(1^{+}\right)$ is equal to

• A. $-1$
• B. $0$
• C. $1$
• D. none of these

Answer 1

The correct option is B $0$

$f^{\prime }\left(1\right)=\underset{h\to 0}{lim}\frac{f(1+h)-f\left(1\right)}{h}=\underset{h\to 0}{lim}\frac{\sin \pi [1+h]-\sin \pi \left[1\right]}{h}=\underset{h\to 0}{lim}\frac{\sin \pi -\sin \pi }{h}=0$
Hence, option 'B' is correct.