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Homework Help: Factoring X Out limit

  1. Nov 6, 2004 #1

    quasar987

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    I Have No Clue How To Start This One. I Tried Applying The Same Kind Of Strategy As In https://www.physicsforums.com/showthread.php?t=51562 But No Luck. Please Give Me A Hint.

    [tex] \lim_{x\rightarrow 0}\frac{\sqrt[4]{1+x^2}-1}{x} [/tex]

    Factoring X Out Gives A [itex]\infty - \infty[/itex] Undeterminate Form. The answer is 0.
     
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  3. Nov 6, 2004 #2

    arildno

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    Set:
    [tex]a=\sqrt[4]{1+x^{2}}, b=1^{\frac{1}{4}}=1[/tex]
    Find the polynomial in a, b P(a,b) which satisfies:
    [tex](a-b)P(a,b)=a^{4}-b^{4}[/tex]
    In order to find P(a,b), use polynomial division on:
    [tex](a^{4}-b^{4}):(a-b)[/tex]

    In order then to evaluate the limit, multiply your fraction with:
    [tex]1=\frac{P(a,b)}{P(a,b)}[/tex]
     
  4. Nov 6, 2004 #3

    quasar987

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    Simply amazing!

    And I realize this method is the same as the one which have been advised to me for the other limit problem, but generalized. Thanks arildno !
     
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