Let f(x)= array cl x^ 2 | x |, & x 0 0, & x=0 array , x R, . then f is
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let \[f(x)=\left\{\begin{array}{cl}
x^{2}\left|\cos \frac{\pi}{x}\right|, & x \neq 0 \\
0, & x=0
\end{array}, x \in R,\right.\] then f is
- differentiable both at x = 0 and at x = 2
- differentiable at x = 0 but not differentiable at x = 2
- not differentiable at x = 0 but differentiable at x = 2
- differentiable at neither at x = 0 nor at x = 2
Answer
(B) differentiable at x = 0 but not differentiable at x = 2
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