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Math Help - Using Definition Of Derivative As A Limit to Calculate...

  1. #1
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    Using Definition Of Derivative As A Limit to Calculate...

    Figured it out, but if you're interested, question is below. It's much easier to do if you solve for f'x not f'2


    f'(2) for the function f(x) = 1/(sqrt(x+2))

    This problem is teasing me. No matter what approach I take, I cannot make all the numerator terms have enough delta x values to cancel with the quotient delta x terms. I have tried deriving f'(2) with no luck. I know what the limit definition of the derivative is, I'm assuming that is my algebra and ability to manipulate equations that is lacking. Any help is appreciated.
    Last edited by evankiefl; January 24th 2011 at 02:24 PM.
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  2. #2
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    \displaystyle \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}

    f(x) = \dfrac{1}{\sqrt{x+2}}

    Hence f(x+h) = \dfrac{1}{\sqrt{x+h+2}}


    \displaystyle \lim_{h \to 0} \dfrac{\dfrac{1}{\sqrt{x+h+2}} - \dfrac{1}{\sqrt{x+2}}}{h}
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