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Math Help - Limit definition and derivative

  1. #1
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    Limit definition and derivative

    If I have to use the limit definition to find the derivative and I have a f(x)= 1/square root(x+a number)....how would I start this off? Do I just leave it the same or do I have to change it? Thanks
    Last edited by Minnesota1; February 11th 2009 at 09:46 PM. Reason: new prob
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  2. #2
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    Quote Originally Posted by Minnesota1 View Post
    If I have to use the limit definition to find the derivative and I have a f(x)= 1/square root(x+a number)....how would I start this off? Do I just leave it the same or do I have to change it? Thanks
    Step 1:multiply by :

    .......... \frac{\sqrt{x+a}}{\sqrt{x+a}} to get:

    ............... \frac{\sqrt{x+a}}{x+a}..............................

    Step 2: form the ratio: \frac{f(x+h)-f(x)}{h} to get,after doing some calculations:


    ................... \frac{(x+a)\sqrt{x+h+a}-(x+h+a)\sqrt{x+a}}{h(x+a)(x+h+a)}.................................................. ......................


    Step 3: multiply by:

    .............. \frac{(x+a)\sqrt{x+h+a}+(x+h+a)\sqrt{x+a}}{(x+a)\s  qrt{x+h+a}+(x+h+a)\sqrt{x+a}} to get after doing some calculations:

    .....................- \frac{ 1}{(x+a)\sqrt{x+h+a}+(x+h+a)\sqrt{x+a}}.................................................. ...................


    Step 4: let h go to zero to get:



    ...................-1/2 \frac{ 1}{(x+a)\sqrt{x+a}} ,which is the desired limit............................................. .....................................
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