If f(x) = sin([pi^2]x) - sin([-pi^2]x),where | vedclass

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(D) Given $f(x) = \sin([\pi^2]x) - \sin([-\pi^2]x)$.Since $\pi^2 \approx 9.869$,we have $[\pi^2] = 9$.Since $-\pi^2 \approx -9.869$,we have $[-\pi^2]

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$f(\pi) = -1$

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(D) Given $f(x) = \sin([\pi^2]x) - \sin([-\pi^2]x)$.Since $\pi^2 \approx 9.869$,we have $[\pi^2] = 9$.Since $-\pi^2 \approx -9.869$,we have $[-\pi^2] = -10$.Thus,$f(x) = \sin(9x) - \sin(-10x) = \sin(9x) + \sin(10x)$.Check options:$A) f(0) = \sin(0) + \sin(0) = 0$ (True).$B) f(\frac{\pi}{2}) = \sin(\frac{9\pi}{2}) + \sin(5\pi) = 1 + 0 = 1$ (True).$C) f(\frac{\pi}{4}) = \sin(\frac{9\pi}{4}) + \sin(\frac{10\pi}{4}) = \sin(\frac{\pi}{4}) + \sin(\frac{5\pi}{2}) = \frac{1}{\sqrt{2}} + 1$ (True).$D) f(\pi) = \sin(9\pi) + \sin(10\pi) = 0 + 0 = 0$. Since $0 
eq -1$,this statement is not true.

If $f(x) = \sin([\pi^2]x) - \sin([-\pi^2]x)$,where $[x]$ denotes the greatest integer function $\leq x$,then which of the following is not true?

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