Curious Function

Calculus Level 5

Consider the function f ( x ) = cos x ln ( x ) + sin x x f(x) = \dfrac{\cos x}{\ln (|x|) } + \dfrac{\sin x}x .

Then what is the behavior of f ( x ) f(x) about the point x = 0 x= 0 ?

Has a jump discontinuity Infinite None of these choices Continuously differentiable Different derivates from the left and from the right Continous

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