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Math Help - Limits, Analytically

  1. #1
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    Limits, Analytically

    Hi, I needed to know to to solve the limit of this equation analytically

    lim
    x->2

    (4-X^2)/(3-√(X^2+5))
    Last edited by DjamaalRobinson; September 11th 2008 at 04:31 PM.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by DjamaalRobinson View Post
    Hi, I needed to know to to solve the limit of this equation analytically

    lim
    x->2

    (4-X^2)/(3-√(X^2+5))
    \lim_{x\to{2}}\frac{4-x^2}{3-\sqrt{x^2+5}}

    The trick here is to multiply this fraction by the conjugate of the denominator:

    \begin{aligned}\lim_{x\to{2}}\frac{4-x^2}{3-\sqrt{x^2+5}}&=\lim_{x\to{2}}\frac{4-x^2}{3-\sqrt{x^2+5}}\cdot{\color{red}\frac{3+\sqrt{x^2+5}  }{3+\sqrt{x^2+5}}}\\ &=\lim_{x\to{2}}\frac{(4-x^2)(3+\sqrt{x^2+5})}{9-(x^2+5)}\\ &=\lim_{x\to{2}}\frac{(4-x^2)(3-\sqrt{x^2+5})}{4-x^2}\\ &=\lim_{x\to{2}}(3+\sqrt{x^2+5})=\dots\end{aligned  }

    Does this make sense?

    --Chris
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  3. #3
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    Wow thanks alot, ive only used conjugates to get rid of i, didnt even think to use it, thnks
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