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!

Find value of a in limit

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Is there a number a such that

    lim
    x -> 2 3x^(2) + ax + a + 3 / x^(2) + x - 2

    exists? If so, find the value of a and the value of the limit.

    2. Relevant equations

    None.

    3. The attempt at a solution

    lim
    x -> 2 (x + 2)(3x + p) / (x + 2)(x-1)

    (factored top containing x + 2, as it has to cancel with the bottem for limit to exist and made 3x + p = rest of polynomial)

    Middle term: 3x 2
    X
    x p

    3xp + 2x = ax
    3p + 2 = a

    constant:

    2p = a + 3
    2p = 3p + 2 + 3
    p = -5

    3(-5) + 2 = a
    a = -13

    but the answer at the back of my book for a was 15
     
  2. jcsd
  3. Apr 24, 2010 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Are you sure the limit is at 2 and not -2? At x= 2, the denominator is 4+ 2- 2= 4, not 0 so this limit exists and is (15+ 3a)/4 for any value of a.

    If the limit is as x goes to -2, then the denominator is 0 and the limit will exist if and only if the numerator is also 0. [itex]3(-2)^2+ a(-2)+ a+ 3= -a+ 15[/itex] so a must be 15.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find value of a in limit
Loading...