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Absolute limits

  1. Sep 12, 2006 #1


    Is this the correct symbolic method to differentiate this formula using the limit definition?

    [tex]f(x) = x|x|[/tex]

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

    [tex]f'(x) = \lim_{h \rightarrow 0} \frac{(x + h)^2 - x^2}{h} = \lim_{h \rightarrow 0} \frac{x^2 + 2hx + h^2 - x^2}{h} = \lim_{h \rightarrow 0} \frac{2hx + h^2}{h} = \lim_{h \rightarrow 0} 2x + h[/tex]
    [tex]\boxed{f'(x) = 2|x|}[/tex]

     
    Last edited: Sep 12, 2006
  2. jcsd
  3. Sep 12, 2006 #2

    shmoe

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    3 cases, x>0, x<0 and x=0.
     
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