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Let K be the set of all real values of x where the function

Question:

Let $\mathrm{K}$ be the set of all real values of $x$ where the function $\mathrm{f}(\mathrm{x})=\sin |\mathrm{x}|-|\mathrm{x}|+2(\mathrm{x}-\pi) \cos |\mathrm{x}|$ is not differentiable. Then the set $K$ is equal to:-

  1. $\{\pi\}$

  2. $\{0\}$

  3. $\phi$ (an empty set)

  4. $\{0, \pi\}$

Correct Option: , 3

Solution:

$f(x)=\sin |x|-|x|+2(x-\pi) \cos x$

$\because \sin |\mathrm{x}|-|\mathrm{x}|$ is differentiable function at $\mathrm{x}=0$

$\therefore \mathrm{k}=\phi$

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