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Homework Help: Divided by highest term in numerator limit

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    lim[itex]\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}[/itex]

    3. The attempt at a solution
    i tried diving by highest term in denominator (4^x), but got me no where.

    the solution manual has: (divided by highest term in numerator.)with the answer is zero which i don't know how.

    lim[itex]_{x->∞}\displaystyle \frac{(\frac{2}{3})^x - 1}{1 + (\frac{4}{3})^x}[/itex] = 0
  2. jcsd
  3. Mar 15, 2013 #2


    Staff: Mentor

    Factor 3x out of the numerator and factor 4x out of the denominator.
  4. Mar 15, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper

    Why didn't dividing by 4^x get you anywhere?
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