JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

f(x)=\left\{\begin{array}{ll}x e^{-\left(\frac{1}{|x|}+\frac{1}{x}\right)} & , x \neq 0 \\ 0 & , x=0\end{array}\right.

then

\mathrm{f}(\mathrm{x})

View answer and explanation

Correct option: C

continuous for all

x

but not differentiable at

x=0

Option C is correct because the function is continuous for all x but not differentiable at x=0 due to unequal left-hand and right-hand derivatives.

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