Q.Let $f(x) = \begin{cases} \frac{\sin 2x}{x} & x \ne 0 \ 2 & x = 0 \end{cases}$ . Then $f$ is

continuous and differentiable at

x=0

continuous but not differentiable at

x=0

not continuous at

x=0

differentiable but not continuous

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

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Q.Let f(x)={sin⁡2xxx≠0 2x=0f(x) = \begin{cases} \frac{\sin 2x}{x} & x \ne 0 \ 2 & x = 0 \end{cases}f(x)={xsin2x​​x=0 2​x=0​. Then fff is