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Limits Continuity and Differentiability question

2023 · 24 Jan · Shift 1 · Q36

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 24 Jan · Shift 1 · Q36

Limits Continuity and Differentiability question

2023 · 24 Jan · Shift 1 · Q36

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f(x) = \left\{ {\begin{matrix} {{x^2}\sin \left( {{1 \over x}} \right)} & {,\,x e 0} \\ 0 & {,\,x = 0} \\ \end{matrix} } \right.

Then at

x=0

A
$f$ is continuous but $f'$ is not continuous
B
$f$ and $f'$ both are continuous
C
$f$ is continuous but not differentiable
D
$f'$ is continuous but not differentiable

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