Question

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

विकल्प

• (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

\[\Rightarrow f(x) = \sin \left[ 9 . 8 \right]x + \sin \left[ - 9 . 8 \right]x\]

\[ \Rightarrow f(x) = \sin 9x - \sin 10x\]

\[f\left( \frac{\pi}{2} \right) = \sin 9 \times \frac{\pi}{2} - \sin 10 \times \frac{\pi}{2}\]

\[ \Rightarrow f\left( \frac{\pi}{2} \right) = 1 - 0 = 1\]