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Limit problem using the formal definition of a derivative

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Use the definition of the derivative to determine if f'(0) exists for the function,

    f(x) = (x^2)sin(1/x) if x is not 0
    0 if x is = 0

    2. Relevant equations

    f'(x) = f(x+h) - f(x)
    ------------
    h

    3. The attempt at a solution

    Starting plugging it all in as usual and got to

    (x^2 +2xh + h^2)(sin(1/x+h)) - (x^2)(sin(1/x)
    ----------------------------------------------
    h

    How do I simplify from here?

    Thanks in advance - I really wanna develop a solid method to solving these.
     
  2. jcsd
  3. Sep 28, 2011 #2

    micromass

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    You're doing it too general know. That is, you're forming the quotient

    [tex]\frac{f(x+h)-f(x)}{h}[/tex]

    But here you know that x=0. So try form the quotient where x=0.
     
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