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D/dx sinc(x)

  1. Jan 21, 2010 #1
    Hey can anyone help me prove that the derivative of sin(x)/x is zero at x=0
     
  2. jcsd
  3. Jan 22, 2010 #2
    A function f:R -> R is differentiable at 0 if
    [tex]\lim_{h \rightarrow 0}\frac{f(h)-f(0)}{h}[/tex]
    exists. You can apply this definition and then use l'Hopital's rule or perhaps some first-order estimates to show that this last limit exists. Alternatively, you can probably work directly with the series expansion for sin.
     
  4. Jan 22, 2010 #3
    `
    But f(0) = sin0/0 is not defined
     
  5. Jan 22, 2010 #4
    Well I took it that the OP actually meant the sinc function, which just extends f(x) = sin(x)/x by continuity so that f(0) = 1.
     
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