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Limits, need help

  1. Mar 15, 2014 #1
    1. The problem statement, all variables and given/known data

    Calculate the limit, if it exists:

    lim x→3+ = 81-x4/(x2-6x+9)2

    2. Relevant equations



    3. The attempt at a solution

    -(x4-81)/(x-3)(x-3)

    = -(x2-9)(x2+9)/(x-3)(x-3)

    = -(x-3)(x+3)(x2+9)/(x-3)(x-3)

    = -(x+3)(x2+9)/(x-3)..............I'm stuck here and don't know what to do next
     
  2. jcsd
  3. Mar 15, 2014 #2
    You've already done the first step: that is to cancel out common factors in the numerator and denominator so that you don't get 0/0.
     
  4. Mar 15, 2014 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You have, as Vahsek said, already cancelled what you could so that you no longer have "0/0" when you set x= 3. What do you get? Remember that the problem was to "Calculate the limit, if it exists".
     
  5. Mar 15, 2014 #4
    By substituting 3 in the denominator, it would be undefined, so their is no limit ?
     
  6. Mar 15, 2014 #5
    Indeed, substituting 3 means that you would have 0 in the denominator, so the original expression would diverge as x → 3+. Therefore, you could argue that there is no limit since the expression would not converge to any real number per say.

    That being said, I feel that a more precise answer is needed. For instance, you could say how it diverges.
     
  7. Mar 15, 2014 #6
    I'm guessing it would go to negative infinity then ?
     
  8. Mar 15, 2014 #7
    That's right!
     
  9. Mar 15, 2014 #8
    Ok, thanks guys for your help :)
     
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