Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By johnsomeone

Math Help - Limit algebra

  1. #1
    Junior Member Greymalkin's Avatar
    Joined
    Jun 2012
    From
    Montreal
    Posts
    74
    Thanks
    1

    Limit algebra

    Please explain to me how:
    \lim_{x\to\--\infty} \frac{3x}{4x-\sqrt{16x^2(1-\frac{3}{16x})}}
    becomes
    \lim_{x\to\--\infty} \frac{3x}{4x-(-4x)\sqrt{(1-\frac{3}{16x})}}

    Bringing 16x2 out from the radical becomes negative because x is approaching negative infinity? I don't quite understand why the other coefficients would not automatically become negative, or more importantly why is this one an exception??. Is there some vast concept at work here, or should I just devote this "rule" to route memorization?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    146

    Re: Limit algebra

    \lim_{x\to\--\infty} \frac{3x}{4x-\sqrt{16x^2(1-\frac{3}{16x})}}

    = \lim_{x\to\--\infty} \frac{3x}{4x-\sqrt{16x^2}\sqrt{(1-\frac{3}{16x})}} (Note both factors under the original square root are positive.)

    = \lim_{x\to\--\infty} \frac{3x}{4x-|4x|\sqrt{(1-\frac{3}{16x})}} (Note that square root sign always means the POSITIVE square root.)

    \lim_{x\to\--\infty} \frac{3x}{4x-(-4x)\sqrt{(1-\frac{3}{16x})}} (Note that x negative, so |x| = -x.)
    Last edited by johnsomeone; October 3rd 2012 at 05:32 AM.
    Thanks from Greymalkin
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: August 17th 2011, 03:41 AM
  2. Replies: 2
    Last Post: September 11th 2010, 10:04 PM
  3. Finding this limit using Algebra
    Posted in the Calculus Forum
    Replies: 10
    Last Post: August 31st 2009, 01:58 PM
  4. Replies: 2
    Last Post: March 11th 2009, 07:21 PM
  5. finding a limit using only algebra
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 19th 2009, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum