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Help with this limit please.

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data
    find the limit of:

    [tex]\lim_{x\rightarrow2}\frac{1}{x-2}-\frac{12}{x^{3}-8}[/tex]




    3. The attempt at a solution

    Any help guys? Should i cross multiply then divide and see what i get or is there something else.(besides l'hospital's rule and taylor series because i haven't learned them yet.)
     
  2. jcsd
  3. Feb 23, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I can't imagine why you would think "cross multiply" here. Of course, what you should do is the subtraction indicated in the problem"
    [tex]\frac{1}{x- 2}- \frac{12}{x^3- 8}= \frac{?}{x^3- 8}[/tex]
     
  4. Feb 23, 2012 #3

    Mark44

    Staff: Mentor

    Cross multiply? You do that when you have an equation that involves two fractions.

    Combine the two fractions, and then go from there. Note that the difference of cubes can be factored: a3 - b3 = (a - b)(a2 + ab + b2).
    L'Hopital's Rule cannot be applied to this problem because what you have is a difference, not a quotient.
     
  5. Feb 23, 2012 #4
    ok i got:

    [tex]\lim_{x\rightarrow2}\frac{x+4}{x^{2}+2x+4}=\frac{1}{2}[/tex]

    is that correct?
     
  6. Feb 23, 2012 #5

    Mark44

    Staff: Mentor

    Yes - perfect!
     
  7. Feb 23, 2012 #6
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