Q.Let $f(x) = \begin{cases} \frac{\sin(\pi x)}{x(x-2)} & x \ne 0,2 \ a & x = 0 \ b & x = 2 \end{cases}$ . For continuity at $x=0$ and $x=2$ , $a$ and $b$ are

\pi/2, \pi/2

\pi/2, -\pi/2

0, 0

\pi, \pi

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.Let f(x)={sin⁡(πx)x(x−2)x≠0,2 ax=0 bx=2f(x) = \begin{cases} \frac{\sin(\pi x)}{x(x-2)} & x \ne 0,2 \ a & x = 0 \ b & x = 2 \end{cases}f(x)={x(x−2)sin(πx)​​x=0,2 a​x=0 b​x=2​. For continuity at x=0x=0x=0 and x=2x=2x=2, aaa and bbb are