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Math Help - Derrivative

  1. #1
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    Derrivative

    Determine whether f'(0) exists.

    f(x)={ xsin(1/x) if x does not =0
    {
    { 0 if x=0
    {


    Sorry but its suposed to be a piecewise function.
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  2. #2
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    Quote Originally Posted by johntuan View Post
    Determine whether f'(0) exists.

    f(x)={ xsin(1/x) if x does not =0
    {
    { 0 if x=0
    {


    Sorry but its suposed to be a piecewise function.
    By definition, f'(0) = \lim_{x\to 0} \frac{f(x) - f(0)}{x - 0} = \lim_{x\to 0} \sin \frac{1}{x}

    But this limit does not exist. Why is that?
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  3. #3
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    because if u plug in x the denominator is 0?
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  4. #4
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    The limit can exist even if the function is not defined at that point..

    ..there is another reason..
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  5. #5
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    im still not too sure but i think it has something to do with the sin right?
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  6. #6
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    Actually there is a point which is seen hard
    Assume if you put in sin1/x any number , it goes a range if you put it in 0 ''zero '' is criticall 1/x x=0 result of this is the infinitesimal sin inf. is not available but if you think that sin x for every x value goes [-1,1] we all know there is no chance for sinx and if we put ( x=inf. ) it always goes between [-1,1] range but none of them is not taken by it so we account its range ''not available'' this equation helps us generally limit and derivative problems
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