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Homework Help: Limit 2*x-sqrt(4*x^2+x+1)

  1. Sep 22, 2010 #1

    Suy

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    1. The problem statement, all variables and given/known data
    lim x->-inf 2*x-sqrt(4*x^2+x+1)


    2. Relevant equations



    3. The attempt at a solution
    For positive inf, i got -inf(not sure)
    but negative inf, i got -1/4
    http://www.wolframalpha.com/input/?i=lim+2*x-sqrt%284*x^2%2Bx%2B1%29
    but wolfram have switch the answer, which is right, so i don't know which part i am wrong
    lim X->-inf
    2*x-sqrt(4*x^2+x+1)
    2*x-sqrt(4*x^2+x+1)*((2*x+sqrt(4*x^2+x+1))/(2*x+sqrt(4*x^2+x+1))
    (4x^2+4x^2-x-1)/(2*x-sqrt(4*x^2+x+1))
    -x-1/(2*x-sqrt(4*x^2+x+1))
    -x/(2x-sqrt(4x^2) X<0 sqrt(4x^2) =|2x|=-2x
    -x/(2x-(-2x))=-1/4

    lim x->+inf
    -x/(2x-sqrt(4x^2) X>0 sqrt(4x^2) =|2x|=2x
    -x/0= -inf?
    Thanks
     
  2. jcsd
  3. Sep 22, 2010 #2

    Mentallic

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    Homework Helper

    Yes, good.

    No, you should have [tex]\frac{4x^2-(4x^2+x+1)}{2x+\sqrt{4x^2+x+1}}[/tex]
    You got the numerator wrong - specifically it should be -4x2 not +4x2. And in the denominator, you changed it to a minus when you showed a plus in the previous line.
     
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