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Math Help - derivatives using limit formula.

  1. #1
    Super Member
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    Santiago
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    517

    derivatives using limit formula.

    use limit formula to find

     <br />
f'(x) = \frac{1}{x^2}<br />

     <br />
lim \frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}<br />

     <br />
lim \frac{\frac{x^2 - (x+h)(x+h)}{x^2(x+h)(x+h)}}{h}<br />

     <br />
lim \frac{\frac{-2xh-h^2}{x^2(x+h)(x+h)}}{h}<br />

     <br />
lim \frac{\frac{h(-2xh-h)}{x^2(x+h)(x+h)}}{h}<br />

    is this correct so far?
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  2. #2
    Senior Member Twig's Avatar
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    Gothenburg
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    396

    hi

    Yes it is.
    Now you can divide with h, so you´re left with:
    \frac{-2x-h}{x^2(x+h)^2}


    \frac{-2x}{x^4 + 2(x^3)h +(x^2)(h^2)}
    This gives you, after you´ve let h \, \rightarrow \, 0
    You also shorten out a x from the numerator and the divisor.
    \frac{-2}{x^3}
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  3. #3
    Super Member
    Joined
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    Santiago
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    Quote Originally Posted by Twig View Post
    Yes it is.
    Now you can divide with h, so you´re left with:
    \frac{-2x-h}{x^2(x+h)^2}


    \frac{-2x}{x^4 + 2(x^3)h +(x^2)(h^2)}
    This gives you, after you´ve let h \, \rightarrow \, 0
    You also shorten out a x from the numerator and the divisor.
    \frac{-2}{x^3}
    thanks mate!!!
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