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Lim x→inf text book example confusing step

  1. Sep 10, 2012 #1
    I was hoping someone could clarify a step of an example in my calculus textbook.

    lim x→∞ (√(2*x2+1))/(3*x-5) = lim x→∞ (√(2+(1/x2)))/(3-(5/x)), (since √x2=x for x>0)

    The description for the step says to divide numerator and denominator by x.

    I understand to divide top and bottom of a rational function by the xn where n is the highest power of x that occurs in the denominator in this situation but I don't understand how the numerators equate in this equation.
     
  2. jcsd
  3. Sep 10, 2012 #2

    Stephen Tashi

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    For x > 0, (1/x) sqrt( 2x^2 + 1) = sqrt(1/x^2) sqrt(2x^2 + 1) = sqrt( (1/x^2)(2x^2 + 1) )
     
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