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Limit question

  1. Jul 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Use this limit for the following problems: lim as h approaches 0 of [f(x+h)-f(x)]/h.

    f(x)=[tex]\sqrt{x}[/tex], x=7

    2. Relevant equations

    3. The attempt at a solution

    lim as h approaches 0 of [f(x+h)-f(x)]/h

    = lim as h approaches 0 of ([tex]\sqrt{7+h}[/tex]-[tex]\sqrt{7}[/tex])/h

    I'm having trouble simplifying the numerator, is there any way to get rid of the square roots in the numerator? Thank you.
  2. jcsd
  3. Jul 25, 2009 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Rationalize the numerator

    [tex] \frac{ (\sqrt{7+h} - \sqrt{7})( \sqrt{7+h} + \sqrt{7})}{h( \sqrt{7+h} + \sqrt{7}}[/tex]
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