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Homework Help: Help solving limits!

  1. Sep 27, 2010 #1
    i know how to solve limits, but i have trouble seeing if i can factor anymore or if the limit just doesn't exist, which is the case with the next few questions

    1. The problem statement, all variables and given/known data

    1/(sqrt(x)-2) - 4/(x-4)

    2. Relevant equations

    3. The attempt at a solution

    this is what i have now, i dont think i can do anything else, but im probably wrong.
    And i have written that the limit doesn't exist.


    and sorry if the equation is written the wrong way or anything, with the square roots and everything!
  2. jcsd
  3. Sep 27, 2010 #2
    I am assuming the limit is as x approaches 4.

    The limit does in fact exist.

    You should try rationalizing , that is,

    [tex] \frac{1}{ \sqrt{x} -2}[/tex] [tex] \frac{ \sqrt{x}+2}{ \sqrt{x}+2}[/tex]
  4. Sep 27, 2010 #3
    yes, it is as x approaches 4, sorry about that.

    but when i rationalize it, wouldn't i just get x-4 in the denominator which would still be division by zero?
    i'll see if i can figure it out considering you said the limit exists, thank you
  5. Sep 27, 2010 #4
    Rationalize and then add what you get to - 4/(x-4).

    They have the same denominator now, right ?

    Then, see if you can factor anything out from the "new" function.
  6. Sep 27, 2010 #5

    and just so i know in the future, how did you get the square root sign?
  7. Sep 27, 2010 #6


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    I didn't get that answer; you're close, though.
  8. Sep 27, 2010 #7
    The answer should be 1/4 .

    I am sure you just made a little sign error.

    The symbols are written from Latex

  9. Sep 27, 2010 #8
    I keep getting -1/4

    I know you guys are right though, i graphed it to make sure, not that i thought you were wrong haha.
    I have no clue where im going wrong though.

    thanks for your help though
  10. Sep 27, 2010 #9
    Show me your steps so I can point out the error.
  11. Sep 28, 2010 #10
    i figured it out, i was rationalizing the left side but i forgot to get a common denominator afterwards.
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