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Tangent at the origin

  1. Oct 11, 2010 #1
    1. The problem statement, all variables and given/known data

    What must hold true for a function to have a tangent at the origin.

    Eg. Given f(x) = 0, x = 0

    and f(x0 = xsin (1/x) x does not equal 0

    will the graph have a tangent at the origin?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 11, 2010 #2

    LCKurtz

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    It must have a finite derivative when x = 0. Check its difference quotient.
     
  4. Oct 12, 2010 #3
    What is a finite derivative?
     
  5. Oct 12, 2010 #4

    LCKurtz

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    Have you had or are you taking calculus? If so then you should know what a derivative is. A function has a finite derivative at a point if its derivative at that point exists and is finite.

    Geometrically this means that the graph of the function is smooth enough at the given point that it has a tangent line that is not vertical.

    To work this problem you need to analyze

    [tex]\lim_{h\rightarrow 0}\frac{f(0+h)-f(0)} h[/tex]

    for your function

    [tex]f(x) = x\sin\frac 1 x,\ f(0)=0[/tex]
     
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