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Homework Help: Find the limit of the sequence as n tends to 1

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the limit of the sequence as n tends to 1

    (3/(1-sqrt(x)) - (2/(1-cuberoot(x))

    2. Relevant equations



    3. The attempt at a solution

    making a common denominator and expanding:
    = lim [tex]\frac{1-3x^{1/3}+2x^{1/2}}{1-x^{1/3}-x^{1/2}+x^{1/6}}[/tex]

    I then divided the whole thing by x^1/2 but didnt get anywhere.
    Any help would be v much appreciated.
    thank you
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 1, 2008 #2

    gabbagabbahey

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    Re: limit

    Simply substituting x=1 into this gives 0/0, so your limit is in one of the forms that qualify for l'hopital's rule...
     
  4. Nov 1, 2008 #3
    Re: limit

    ok,thanks so i used L'hospital's rule and got that the limit is 0; is that right?
     
  5. Nov 1, 2008 #4

    gabbagabbahey

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    Re: limit

    Nope, you shouldn't be getting zero...there is actually an error in your first post: [tex]x^{1/3}x^{1/2}=x^{1/3+1/2}=x^{5/6} \neq x^{1/6}[/tex]

    You will have to use L'hopistal's rule twice
     
  6. Nov 1, 2008 #5
    Re: limit

    you're right
    but in that case, when i use l'hospitals rule once, i get 0/-0.5 = 0
    so why must i use l'hospital's rule again?
     
  7. Nov 1, 2008 #6

    gabbagabbahey

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    Re: limit

    You should be getting 0/0 after the first time (5/6-1/3-1/2=0 not -0.5)
     
  8. Nov 1, 2008 #7
    Re: limit

    Oh my, im so stupid!!! i should have known that.
    Yep, i see my mistake.
    L'hospital's rule twice gives limit =1/2
    right?
     
  9. Nov 1, 2008 #8

    gabbagabbahey

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    Re: limit

    Yup! :smile:
     
  10. Nov 1, 2008 #9
    Re: limit

    Thanks.
     
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