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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.

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


    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
    -1/4?


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

    eumyang

    User Avatar
    Homework Helper

    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

    https://www.physicsforums.com/misc/howtolatex.pdf
     
  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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