Question

If ѓ(x) = sin $\left\{ \frac{\pi}{3}\lbrack x\rbrack - x^{2} \right\}$ for 2 < x < 3 and [x] denotes the greatest integer less than or equal to x, then ѓў ($\sqrt{\pi/3}$) is equal to –

• A. $\sqrt{\pi/3}$
• B. –$\sqrt{\pi/3}$
• C. –$\sqrt{\pi}$
• D. None of these

Answer 1

Answer: (B)

–$\sqrt{\pi/3}$

Answer 2

Q 2 < x < 3

\ [x] = 2

then ƒ(x) = sin $\left\{ \frac{2\pi}{3} - x^{2} \right\}$

\ Ģ(x) = cos $\left( \frac{2\pi}{3} - x^{2} \right)$ (Р2x)

\ Ģ$\left( \sqrt{\frac{\pi}{3}} \right)$ = cos $\left( \frac{2\pi}{3} - \frac{\pi}{3} \right)$ $\left( - 2\sqrt{\frac{\pi}{3}} \right)$

= $\frac{1}{2}$ . $\left( - 2\sqrt{\frac{\pi}{3}} \right)$

= –$\sqrt{\frac{\pi}{3}}$.