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Question
The function \[f\left( x \right) = \frac{\sin \left( \pi\left[ x - \pi \right] \right)}{4 + \left[ x \right]^2}\] , where [⋅] denotes the greatest integer function, is
Options
continuous as well as differentiable for all x ∈ R
continuous for all x but not differentiable at some x
differentiable for all x but not continuous at some x.
none of these
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Solution
(a) continuous as well as differentiable for all x ∈ R
Here,
Since, we know that
Thus, f(x) is a constant function and it is continuous and differentiable everywhere.
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