Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit to Infinity with Sqrt in Denom.(Is this correct?)

  1. Oct 13, 2011 #1
    Lim
    x→∞ [itex]\frac{7x^2-14x+7}{\sqrt{2x^4-4x^3+x+7}}[/itex]

    Normally wouldn't have an issue here, just slightly confused by the sqrt.

    Attempted solution:

    [itex]\frac{7x^2-14x+7}{\sqrt{2x^4-4x^3+x+7}}*\frac{x^-2}{x^-2}[/itex]

    Yields [itex]\frac{7}{\sqrt{2}}[/itex]

    Is this correct?

    Similarly:

    lim
    x→-∞
    [itex]\frac{x^3+x+1}{\sqrt{2x^6+x^3+x+3}}[/itex]

    Yields [itex]\frac{1}{\sqrt{2}}[/itex]

    and
    lim
    x→-∞
    [itex]\frac{x^2+x+1}{\sqrt{2x^4+x^3+x+3}}[/itex]

    Yields [itex]\frac{1}{\sqrt{2}}[/itex]
     
  2. jcsd
  3. Oct 13, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    This is correct. The proof to all of that is to forcibly divide both the numerator and the denominator by x to the power of the highest term in the non-square rooted expression and then take the limit to infinity.
     
  4. Oct 13, 2011 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    By the way, use x^{-2} to get [itex]x^{-2}[/itex]. x^-2 puts only the "-" in the exponent: [itex]x^-2[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit to Infinity with Sqrt in Denom.(Is this correct?)
  1. Limit on infinity (Replies: 7)

Loading...