If f(x)= [ ^2]x+ [- ^2]x, where [x] denotes the greatest integer … - Vidyadip

MCQ

If $\text{f(x)}=\sin[\pi^2]\text{x}+\sin[-\pi^2]\text{x},$ where $[x]$ denotes the greatest integer less than or equal to $x,$ then:

✓
$\text{f}\Big(\frac{\pi}{2}\Big)=1$
B
$\text{f}(\pi)=2$
C
$\text{f}\Big(\frac{\pi}{4}\Big)=-1$
D
None of these.

✓

Answer

Correct option: A.

$\text{f}\Big(\frac{\pi}{2}\Big)=1$

$\text{f(x)}=\sin[\pi^2]\text{x}+\sin[-\pi^2]\text{x}$
$\Rightarrow\text{f(x)}=\sin\big[9.8\big]\text{x}+\sin\big[-9.8\big]\text{x}$
$\Rightarrow\text{f(x)}=\sin9\text{x}-\sin10\text{x}$
$\Rightarrow\text{f}\Big(\frac{\pi}{2}\Big)=\sin9\times\frac{\pi}{2}-\sin10\times\frac{\pi}{2}$
$\Rightarrow\text{f}\Big(\frac{\pi}{2}\Big)=1-0=1$

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