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Determine whether f '(0) exists.

f(x) = {xsin(10/x) if x can not = 0
0 if x=0

  • calculus -

    consider the function g(x)=sin(10x)/x as x>>inf clearly this has a limit of zero.

    Is this not the same function in the limit as f(x)?

  • calculus -

    You can prove that limx>0 of (f(x)=limx>inf f(1/x)

    I should have made that clear.

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