Q.The function $f(x) = \begin{cases} \frac{\sin x}{x} \cos(\frac{1}{x}) & x \ne 0 \ 0 & x = 0 \end{cases}$ 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.The function f(x)={sin⁡xxcos⁡(1x)x≠0 0x=0f(x) = \begin{cases} \frac{\sin x}{x} \cos(\frac{1}{x}) & x \ne 0 \ 0 & x = 0 \end{cases}f(x)={xsinx​cos(x1​)​x=0 0​x=0​ is