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  4. Let g(x) = x f(x), where f(x) = begincases x sin (1/x) , x ≠ 0 0 , x = 0 endcases. At x = 0

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Q. Let g(x) = x f(x), where $ f(x) = \begin{cases} x \sin \frac{1}{x} , & x \neq 0 \\ 0 , & x = 0 \end{cases}$. At x = 0

JEE MainJEE Main 1994Continuity and Differentiability

Solution:

Correct answer is (a) g is differentiable but g' is not continuousCorrect answer is (b) g is differentiable while f is not