Q.Let $f(x) = \begin{cases} \frac{\tan(\pi x) - \tan(\pi/4)}{x - 1/4} & x \ne 1/4 \ k & x = 1/4 \end{cases}$ . For continuity at $x=1/4$ , $k$ equals

\pi

2\pi

\pi/2

\pi \sec^2(\pi/4)

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

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Q.Let f(x)={tan⁡(πx)−tan⁡(π/4)x−1/4x≠1/4 kx=1/4f(x) = \begin{cases} \frac{\tan(\pi x) - \tan(\pi/4)}{x - 1/4} & x \ne 1/4 \ k & x = 1/4 \end{cases}f(x)={x−1/4tan(πx)−tan(π/4)​​x=1/4 k​x=1/4​. For continuity at x=1/4x=1/4x=1/4, kkk equals