Q.If $f(x) = \begin{cases} \dfrac{\sin 2x}{x} \cos(\dfrac{1}{x}) & x \ne 0 \ 0 & x = 0 \end{cases}$ , then $f$ is

continuous but not differentiable at

x=0

differentiable at

x=0

discontinuous at

x=0

none

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

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Q.If f(x)={sin⁡2xxcos⁡(1x)x≠0 0x=0f(x) = \begin{cases} \dfrac{\sin 2x}{x} \cos(\dfrac{1}{x}) & x \ne 0 \ 0 & x = 0 \end{cases}f(x)={xsin2x​cos(x1​)​x=0 0​x=0​, then fff is