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Thread: another limit

  1. #1
    Junior Member
    Nov 2008
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy

    another limit

    can someone please show me how to solve
    lim x->2 $\displaystyle \frac{x^2-4x+4}{x^3-3x^2+4}$?
    i think u have to use L'Hopitals, but im not sure. and im not clear on L'Hops, either
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  2. #2
    Feb 2009
    Yes you can use l'hospitals.

    OR you can see that x = 2 is a root/divisor of both polynomials,
    so factoring would break this limit.

    L'hopitals Rule is easier because all you have to do it differentiate the top and bottom polynomial twice.

    You arrive at the expression

    $\displaystyle \frac{2}{6x-6} = \frac{1}{3}$ as x-->2
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