Question

If f(x) = sin [π²] x + sin [−π]² x, where [x] denotes the greatest integer less than or equal to x, then

(a) f(π/2) = 1
(b) f(π) = 2
(c) f(π/4) = −1
(d) None of these

Answer 1

(a) f(π/2) = 1

f(x) = sin [π²] x + sin [−π²]x
$$\begin{gathered} \Rightarrow f\left(x\right)=\sin \left[9.8\right]x+\sin \left[-9.8\right]x \\ \Rightarrow f\left(x\right)=\sin 9x-\sin 10x \\ f\left(\frac{\mathrm{\pi }}{2}\right)=\sin 9\times \frac{\mathrm{\pi }}{2}-\sin 10\times \frac{\mathrm{\pi }}{2} \\ \Rightarrow f\left(\frac{\mathrm{\pi }}{2}\right)=1-0=1 \end{gathered}$$