1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Factoring X Out limit

  1. Nov 6, 2004 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I Have No Clue How To Start This One. I Tried Applying The Same Kind Of Strategy As In https://www.physicsforums.com/showthread.php?t=51562 But No Luck. Please Give Me A Hint.

    [tex] \lim_{x\rightarrow 0}\frac{\sqrt[4]{1+x^2}-1}{x} [/tex]

    Factoring X Out Gives A [itex]\infty - \infty[/itex] Undeterminate Form. The answer is 0.
     
  2. jcsd
  3. Nov 6, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Set:
    [tex]a=\sqrt[4]{1+x^{2}}, b=1^{\frac{1}{4}}=1[/tex]
    Find the polynomial in a, b P(a,b) which satisfies:
    [tex](a-b)P(a,b)=a^{4}-b^{4}[/tex]
    In order to find P(a,b), use polynomial division on:
    [tex](a^{4}-b^{4}):(a-b)[/tex]

    In order then to evaluate the limit, multiply your fraction with:
    [tex]1=\frac{P(a,b)}{P(a,b)}[/tex]
     
  4. Nov 6, 2004 #3

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Simply amazing!

    And I realize this method is the same as the one which have been advised to me for the other limit problem, but generalized. Thanks arildno !
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Factoring X Out limit
  1. Limit of (sin 5x)/x (Replies: 1)

Loading...