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Basic (?) limit problem.

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the limit of [tex](x-3)/(\sqrt{1+x}-2)[/tex] as x tends to 3


    2. Relevant equations
    Conjugate multiplication.


    3. The attempt at a solution

    [tex](x-3)(\sqrt{1+x}+2)/(\sqrt{1+x}-2)(\sqrt{1+x}+2)[/tex]

    [tex](x\sqrt{1+x}+2x-3\sqrt{1+x}-6)/x-3[/tex]

    This is where i get stuck, Im thinking to get rid of the x in the denominator but the -6 in the numerator is what stumps me. Am i supposed to just factor the top somehow?
     
  2. jcsd
  3. Oct 9, 2009 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Don't multiply the numerator out. You have a factor of x - 3 to work with.
     
  4. Oct 9, 2009 #3

    Mark44

    Staff: Mentor

    When you multiply by 1 in the form of (sqrt(1 + x) + 2) over itself, you should get
    [tex]\frac{(x - 3)(\sqrt{1 + x} + 2}{x - 3}[/tex]

    I think you made a mistake in multiplying your original denominator by its conjugate.
     
  5. Oct 9, 2009 #4
    Oh man, how could I not see that. Thanks!
     
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