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!

Limit of a function with absolute value of polynomial in a quotient

  1. Dec 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Lim | x2+x-12 |-8 / (x-4)
    x --> 4

    2. Relevant equations

    3. The attempt at a solution
    My answer is 9.
    It it right ?
    or there is not a limit for F(x) when x --> 4
  2. jcsd
  3. Dec 19, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Limit

    Can we assume you mean [itex]\lim_{x\rightarrow 4} \left(\left|x^2+ x-12\right|- 8\right)/\left(x- 4\right)[/itex]?

    Close to 4, [itex]x^2+ x- 12[/itex] is close to +8 so the absolute value is not needed.
    [itex]x^2+ x- 12- 8= x^2+ x- 20= (x- 4)(x+ 5)[/itex] so [itex]\left(\left|x^2+ x-12\right|- 8\right)/\left(x- 4\right)= (x-4)(x+5)/(x-4)[/itex]. That, of course, has limit 4+ 5= 9 at x= 4.

    If, however, you meant
    [tex]|x^2+ x- 12|- \frac{8}{x- 4}[/tex]
    which what you actually wrote, that has no limit at x= 4.
  4. Dec 19, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    Re: Limit

    Of course, without a calculation or proof, no answer is really right :P
    Did you sketch the graph, for instance? How can you see there whether there is a limit or not, as x --> 4?

    I think it is 9 too, actually.
  5. Dec 19, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    Hi UNknown 2010! :smile:

    Yes, 9 is right :smile:

    I assume it's the | | that's worrying you?

    But it makes no difference at x = 4 (beacuse it's nowhere near 0 there).

    It would make a difference, and there would be no limit, if it were | x2+x-20 | / (x-4) :wink:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Limit of a function with absolute value of polynomial in a quotient