Results 1 to 3 of 3

Math Help - Limits Question

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    21

    Limits Question

    So this question is from one of my review practice problems for my midterm and there's no answer part for it and I was wondering how this question would be solved.

    Lim x -> infinity 5x^3-2x+1 / x^4-x^3+5

    Thanks!

    edit: thank you!
    Last edited by kelvinly; September 30th 2010 at 09:29 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
     \displaystyle \lim_{x\rightarrow \infty} \frac{5x^3 - 2x + 1}{x^4 - x^3 + 5}

    For questions like these (polynomials on the bottom), it helps to divide the numerator and denominator by term in the denominator with the highest power of x. In this case,  x^4

    So we have

     \displaystyle \lim_{x\rightarrow \infty} \frac{\frac{5}{x} - \frac{2}{x^3} + \frac{1}{x^4}}{1 - \frac{1}{x} + \frac{5}{x^4}}

    You can apply the limit to each individual term in both the numerator and denominator.

    Now any fraction of form  \frac{a}{x^n} \rightarrow 0 as  x\rightarrow \infty for any real number a and positive integer n

    You should get the resulting fraction  \frac{0-0+0}{1-0+0} = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853
    Using exactly Gusbob's method in general you can get:

    \displaytype\lim_{x\to\infty}\frac{ax^n+ bx^{n-1}+ \cdot\cdot\cdot+ c}{ux^m+ vx^{m-1}+ \cdot\cdot\cdot+ w}is equal to

    i) infinity if n> m (numerator has higher degree)

    ii) 0 if m< m (denominator has higher degree)


    iii) \frac{a}{u} if m= n. (numerator and denominator have same degree)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limits question.
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: June 22nd 2010, 07:00 AM
  2. Limits question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 2nd 2010, 07:56 PM
  3. Limits Question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 30th 2009, 05:49 PM
  4. Limits question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 5th 2009, 06:35 AM
  5. Limits Question!!!
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 1st 2008, 06:42 PM

/mathhelpforum @mathhelpforum