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Which of the following are differentiable at $x=1$?

I. $f(x)=\cfrac{\ln x}{\sin x}$ II. $f(x)=|x^3-3x+2|$ III. $f(x)=\sqrt{(x-1)^2+0.001} +|x|$

I. $f(x)=\cfrac{\ln x}{\sin x}$

II. $f(x)=|x^3-3x+2|$

III. $f(x)=\sqrt{(x-1)^2+0.001} +|x|$

None

I only

I and II only

I, II, and III