1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Factor out the x

  1. Sep 27, 2007 #1
    1. The problem statement, all variables and given/known data
    lim x->2 (x^3-2x)/(x-2)

    i have done this one thousand ways.... factor out the x, multiply top and bottom by (x-2) and (x+2)... i have tried lots of things but i can't get it to work, any tips how to start this off?
     
  2. jcsd
  3. Sep 27, 2007 #2

    bel

    User Avatar

    Try long division and then express the remainder term as a rational function, and then apply L'hopital's rule to it.
     
  4. Sep 27, 2007 #3
    yeah, we definately haven't gone that far...
     
  5. Sep 28, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    Long division of polynomials is just like normal long division and many tutorials are on the internet. Using it we get the following result: [tex]\frac{x^3-2x}{x-2} = x^2 + 2x+ 2 + \frac{4}{x-2}[/tex].

    You should check it by expanding the right hand side.

    The first part, the polynomial, evaluates to 10. The fraction's denominator goes to zero, so that part goes to infinity. Hence the limit does not exist (the function approaches infinity as x approaches 2).

    bel, you can't apply L'hopital's rule to the ration function because it does not fit any of the indeterminate forms. Using it leads to an incorrect result.
     
  6. Sep 28, 2007 #5
    The first thing you should do with a limit is to put the number in, completely ignoring the fact that it's a limit. If you get something like x/0 where x isn't 0, then no fooling about with anything will make that limit finite. So in this case, the limit is simply infinite.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Factor out the x
  1. [how to factor ] X^ 4 (Replies: 3)

  2. Factorizing X^4 + 1 (Replies: 11)

Loading...