Let f(x) = \ x² sin (1/x), x ≠ 0 0, x = 0. 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

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 24 Jan, Morning shift · Q4212

JEE Main 202324 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

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

Then at

x=0

JEE Main 2023 · 24 Jan, Morning shift · Q4212

JEE Main 202324 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

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

Then at

x=0