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Math Help - Find this limit

  1. #1
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    Find this limit

    (x^-2 - 3^-2)/ (x-3)

    find the limit as x approaches 3

    i've tried changing the exponents into radical form so i can multiply the top and bottom by the conjugate but i can't seem to make it work.. can someone solve this for me please?
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  2. #2
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    \displaystyle \frac{x^{-2} - 3^{-2}}{x - 3} = \frac{\frac{1}{x^2} - \frac{1}{3^2}}{x - 3}

    \displaystyle = \frac{\frac{3^2 - x^2}{3^2x^2}}{x - 3}

    \displaystyle = \frac{(3 - x)(3 + x)}{3^2x^2(x - 3)}

    \displaystyle = \frac{-(x - 3)(3 + x)}{3^2x^2(x - 3)}.


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