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Limit as x goes to infinity (algebraic)

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    limx->infinity (x+2)/(sqrt(81x^2+15))

    2. Relevant equations

    3. The attempt at a solution
    The only thing i could think of doing was rationalizing the denominator to get (x+2)sqrt(81x^2+15) / 81X^2+15 however im pretty sure this is the wrong route cause there doesnt seem to be anywhere to go from here.

    Any help would be greatly apprciated :D the only problems i seem to ever have difficulty with are with roots in the numerator or denominator. any info in that regard would be of use as well.
  2. jcsd
  3. Oct 16, 2008 #2
    divide top and bottom by x and write an x inside the root
  4. Oct 16, 2008 #3
    what exactly do you mean by write an x inside the root. if i divide top and bottom by x i get ((x+2)/x) / ((sqrt(81x^2+15))/x). from here im stuck again
  5. Oct 16, 2008 #4
    alright its 1/9
  6. Oct 16, 2008 #5
    note that this trick generalizes to all rational polynomial limits to infinity, just divide by the highest factor.
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