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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1
Let f,g:R→R\mathrm{f}, \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R} be two functions defined by
f(x)={xsin⁡(1x),x≠00,,x=0, and g(x)=xf(x)f(x)=\left\{\begin{array}{ll} x \sin \left(\frac{1}{x}\right), x \neq 0 \\ 0, & , x=0 \end{array}, \text { and } g(x)=x f(x)\right.

Statement I: ff is a continuous function at x=0\mathrm{x}=0.
Statement II: gg is a differentiable function at x=0\mathrm{x}=0.
View answer and explanation
Correct option: C
Statement I\mathrm{I} is true, statement II is false.
Option C is correct because f(x) is continuous at x=0, but g(x) is not differentiable at x=0.

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