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

continuous and differentiable everywhere

continuous everywhere but not differentiable at

x=0

differentiable everywhere except 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)={sin⁡xxx≠0 1x=0f(x) = \begin{cases} \frac{\sin x}{x} & x \ne 0 \ 1 & x = 0 \end{cases}f(x)={xsinx​​x=0 1​x=0​ is