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Forgotten how to solve for square roots

  1. Apr 22, 2013 #1
    1. The problem statement, all variables and given/known data

    compute f'(x) using the limit definition.

    f(x) = [itex]\sqrt{x}[/itex]

    2. Relevant equations

    f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{f(x+h)-f(x)}{h}[/itex]

    3. The attempt at a solution

    Plugging in the function values gives you

    f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{\sqrt{(x+h)}-\sqrt{x}}{h}[/itex]

    The end result is [itex]\frac{1}{2\sqrt{x}}[/itex] according to answer key.

    I'm not sure how to go about solving. It's the square roots that are screwing me up. I have forgotten how to solve for square roots.

    I've solved 6 problems within this context before coming across this one.
  2. jcsd
  3. Apr 22, 2013 #2


    Staff: Mentor

    Try multiplying by the conjugate over itself. IOW, multiply by
    $$ \frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}$$
  4. Apr 22, 2013 #3
    Understood. I got the answer now. Ty
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