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Limit of 0/0 type

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    lim x->2 (t^3 - 8)/(t^4 - 16)

    2. Relevant equations

    3. The attempt at a solution
    Well, i just cant find the common factor in the numerator and denomenator. I can split (t^4 - 16) to (t^2 - 2)^4 but i cant find any other factors in the numerator.

    Thx for any help :)
  2. jcsd
  3. Oct 21, 2009 #2
    multiply by a conjugate or try (t^2+4)(t^2-4)
  4. Oct 21, 2009 #3
    There's a rather obvious common factor there. Try factorising 8 and 16.
    Alternatively you could use l'Hôpital's rule
  5. Oct 21, 2009 #4
    Yeah i tried (t^2+4)(t^2-4), but i cant find the same factor in the numerator. The t^3 term complicates the matter cause what can i multiply with itself to get t^3 without getting a more complicated factor.. In other words, im unable to express; (t^3 - 8) in any other way.

    I tried conjugate but didnt work for me, and we didnt learn L'Hopitals yet so not allowed to ues it.
  6. Oct 21, 2009 #5


    Staff: Mentor

    t4 - 16 [itex]\neq[/itex](t2 - 2)4
    Note that the polynomial on the left side is of degree 4, while the one on the right is of degree 8. That should have been a clue that something is wrong.

    You should be thinking "difference of squares" and "difference of cubes" for your factoring.
  7. Oct 21, 2009 #6


    Staff: Mentor

    t2 - 4 can be factored. Also, the difference of cubes can be factored. a3 - b3 = (a - b)(a2 + ab + b2).
  8. Oct 21, 2009 #7
    Ah, yeah, i was thinking that it would equal to (t^2 - 4)^2 but the minus sign would be different among the factors.

    Anyway i still cant figure it out, can u help me a bit more :p?
  9. Oct 21, 2009 #8
    now i think i got it.. thanks a lot! :D
  10. Oct 21, 2009 #9
    Ok i found that (t-2)(t^2 +2t +4) = t^3 - 8, and now the two t-2 factors in the numerator and denomenator cancels. however im still stuck with (t^2 - 4) factor which tends to 0 while t tends to 2. So im stuck again.

    If someone could just solve the: lim x->2 (t^3 - 8)/(t^4 - 16) itd be of great help.
    Last edited: Oct 21, 2009
  11. Oct 21, 2009 #10


    Staff: Mentor

    Then your factoring of t4 - 16 is incorrect. Show me how you factored this.
  12. Oct 21, 2009 #11
    you are right, ok i finally solved it. Thanks :)
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