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Let $f(x)=\begin{cases}x^{p}cos\frac{1}{x},x\ne0\\ 0,x=0\end{cases}$ Then $f(x)$ is differentiable at $x=0$ if}

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Continuity requires $p > 0$. Differentiability requires one extra power, so $p > 1$.

Updated On: Jul 3, 2026

$P>0$
$P=0$
$P>1$
$P<1$

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The Correct Option is C

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