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Calculus 1 Homework problem - Find limit without L'Hospital's Rule

  1. Sep 4, 2014 #1
    1. The problem statement, all variables and given/known data

    Lim ( 5+6x2)/(√(x3)) + 2x2 +1)
    x->∞

    2. Relevant equations

    not allowed to use lhopitals rule

    3. The attempt at a solution

    first, i divided by x2, which yielded

    (5/(x2) + 6 + √(x)) / (2 + 1/x2 )

    then i assumed that thelim x--> infi of 5/x2 = 0, lim x--> infi 6 = 6, lim x---> infi sqrt(x) = infinity, lim x--- > infi 2 = 2, lim x---> infi 1/x2 = 0

    so basically i ended up with the limit = to (6(∞))/(2) which im not sure if its the right answer. pretty sure it isnt
     
    Last edited: Sep 4, 2014
  2. jcsd
  3. Sep 4, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You wrote
    [tex] \lim_{x \to \infty} 5 + \frac{6x^2}{\sqrt{x^3}+ 2x^2+1}[/tex]
    If you really mean this, OK, it can stand as written. However, if you mean
    [tex] \lim_{x \to \infty} \frac{5 + 6x^2}{\sqrt{x^3}+ 2x^2+1}[/tex]
    then you absolutely MUST use parentheses, like this:
    (5+6x^2)/(sqrt(x^3) + 2x^2 +1).
     
  4. Sep 4, 2014 #3
    edited* whoops, thanks
     
  5. Sep 4, 2014 #4

    Mark44

    Staff: Mentor

    You need a pair of parentheses around the two terms in the numerator.
    This is a good approach, but you lost a term in the denominator. There should be three terms in the denominator, not two. BTW, √(x3) is the same as x√x.
    Correct, it's not the right answer. Your answer should not have ∞ in it unless the limit is actually infinity. Otherwise, we don't do arithmetic with infinity.
     
  6. Sep 4, 2014 #5
    oh gosh... so the missing term would be sqrt(x)/x, which would have a limit of 0 as it approaches infinity, due to the bottom scaling at a squared rate compared to the top? leaving the final limit as x approaches infinity as 3
     
    Last edited: Sep 4, 2014
  7. Sep 5, 2014 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that is correct. Roughly, the "dominating term" (the term with the highest power) in the both numerator and denominator is the [itex]x^2[/itex] term and the ratio of their coefficients is 6/2= 3.
     
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