Results 1 to 3 of 3

Math Help - Delta Epsilon Proof Help

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    philadelphia
    Posts
    1

    Delta Epsilon Proof Help

    Hi I need to prove

    lim (x-3)/(x2+1) as x goes to infinity is zero using the formal definitional. Can anyone help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2013
    From
    lima
    Posts
    23
    Thanks
    2

    Re: Delta Epsilon Proof Help

    Sucks I would L'Hop the out of it
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328

    Re: Delta Epsilon Proof Help

    Why in the world would you even use L'Hopital? If you could use any method, it's obvious that the denominator is going to infinity faster than the numerator.

    However, since you are required to use the "formal definition", You want to show that, for any \epsilon> 0, we can find \delta> 0 such that if x> \delta, then \left|\frac{x- 3}{x^2+ 1}\right|< \epsilon.

    We can start by writing that as -\epsilon< \frac{x- 3}{x^2+ 1}\right|< \epsilon. It is certainly true that x^2+ 1> 0 for all x so that is the same as -\epsilon(x^2+ 1)< x- 3< \epsilon(x^2+ 1). And then \epsilon x^2- x+ \epsilon+ 3> 0. Solve that quadratic equation and keep the larger root to see how large x must be in order that all this (which is reversible so you can go back to \left|\frac{x- 3}{x^2+ 1}\right|< \epsilon) be true.
    Last edited by HallsofIvy; February 19th 2013 at 06:43 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] epsilon delta proof
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 7th 2011, 06:21 PM
  2. Solving Delta Epsilon Proof (Given Epsilon)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 15th 2010, 03:42 PM
  3. Epsilon - Delta proof help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 13th 2010, 09:55 AM
  4. Replies: 0
    Last Post: October 27th 2009, 07:06 AM
  5. need help on delta epsilon proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 23rd 2009, 05:33 PM

Search Tags


/mathhelpforum @mathhelpforum