Q.Let $f(x) = \begin{cases} \dfrac{x \sin(\pi x)}{ \tan(\pi x) } & x \ne \text{integer} \ 0 & x = \text{integer} \end{cases}$ . Then $f$ is

continuous and differentiable at every integer

continuous at every integer but not differentiable at integers

discontinuous at every integer

none of the above

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

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Q.Let f(x)={xsin⁡(πx)tan⁡(πx)x≠integer 0x=integerf(x) = \begin{cases} \dfrac{x \sin(\pi x)}{ \tan(\pi x) } & x \ne \text{integer} \ 0 & x = \text{integer} \end{cases}f(x)={tan(πx)xsin(πx)​​x=integer 0​x=integer​. Then fff is