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Limit Problem

  1. Sep 9, 2008 #1
    I was working out a limit problem and even though I solved it using L'hospital's rule, I do not know how to solve it another way which was probably the intended way. Here's the limit:

    [tex]\lim_{x\rightarrow2} \frac{x^4 - x^3 + x^2 - 4x - 4}{2x^2 - 5x + 2}[/tex]

    So I used L'hospital's rule and got 20/3 but I want to know another method.

  2. jcsd
  3. Sep 9, 2008 #2


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    The numerator and denominator have a common factor of (x-2) that is causing it to have a 0/0 form. If you cancel out that common factor, you can just put x=2.
  4. Sep 9, 2008 #3
    Yeah I figured that was the case, but I wasn't able to factor it out in the numerator.
  5. Sep 9, 2008 #4


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    Just do polynomial division of (x-2) into the numerator. You know you'll get zero remainder, right?
  6. Sep 9, 2008 #5
    Doh! Lol, I completely forgot about synthetic division.
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