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Limit of a rational function with a square-rooted expression in numerator.

  1. Jun 26, 2011 #1
    lim as x -> 0, [(x+4)1/2-2]/x

    That's the limit I want to evaluate. I keep running into problems getting to the real limit (1/4).
    You don't have to give me the answer, but let me know if I'm missing something simple. Or you can just give me a hint.
     
  2. jcsd
  3. Jun 26, 2011 #2

    gb7nash

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    What have you tried so far?
     
  4. Jun 26, 2011 #3
    So far I have tried dividing out by (x+4)1/2. This still gives me an x in the denominator that yields infinity when x->0.

    I have also tried dividing out by x, but this gives me fractions in the numerator that, again, give me infiinity.
     
  5. Jun 26, 2011 #4

    gb7nash

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    Have you learned l'hopital's rule yet?
     
  6. Jun 26, 2011 #5
    Yea, but I was able to get the answer by just rationalizing the numerator. I'm gonna try l'Hospital now.

    EDIT: I thought we only use l'Hospital's rule for lmits that are 0/0 or inf/inf.
     
  7. Jun 26, 2011 #6

    gb7nash

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    Both methods should work. l'hopital's rule will probably be easier, but rationalizing the numerator is good practice.
     
  8. Jun 26, 2011 #7
    But aren't we using l'Hospital's rule for indeterminate forms?
     
  9. Jun 26, 2011 #8

    gb7nash

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    You can use l'hopital's rule for 0/0 or +-inf/inf (which in this case you get 0/0). I was just saying there's more than one way of getting the right answer.
     
  10. Jun 26, 2011 #9
    gb7: Yea, I'm an idiot for not noticing that. Thanks for the help!
     
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