Let g ( x ) = x f ( x ), where f(x)= array cl x 1 x , & x 0 0, & x=0 array . At x=0 .
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let g(x) = x f (x), where \[f(x)=\left\{\begin{array}{cl}
x \sin \frac{1}{x}, & x \neq 0 \\
0, & x=0
\end{array} \text {. At } x=0\right.\]
- g is differentiable but g
- g is differentiable while f is not
- both f and g are differentiable
- g is differentiable and g
Answer
(D) g is differentiable and g ′ is continuous
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