Q.The function $f(x) = \begin{cases} x \sin(1/x) & x \ne 0 \ 0 & x = 0 \end{cases}$ is

continuous and differentiable at

x=0

continuous but not differentiable at

x=0

differentiable but not continuous at

x=0

neither continuous nor differentiable at

x=0

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

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Q.The function f(x)={xsin⁡(1/x)x≠0 0x=0f(x) = \begin{cases} x \sin(1/x) & x \ne 0 \ 0 & x = 0 \end{cases}f(x)={xsin(1/x)​x=0 0​x=0​ is