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!

Rationalizing cubed expressions

  1. Nov 19, 2007 #1
    I know how to rationalize most equations when trying to find limits. However, this problem seem give me trouble.

    (((1+x)^3)-1)/x as x approaches 0

    I tried the method of multiplying by the conjugate but it doesn't seem to get me anywhere. Mainly its the cubed (1+x) that troubles me.
     
  2. jcsd
  3. Nov 19, 2007 #2
    So you don't want to just expand it traditionally and simplify? You want some sort of easy trick (like multiplying by the conjugate and whatnot)?
     
  4. Nov 19, 2007 #3
    Could you elaborate and show me how I could expand it traditionally and solve. Maybe I'm just over tired but i can't see how that would work.
     
  5. Nov 19, 2007 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I don't see anything to rationalize. Just expand (1+x)^3 subtract 1 and divide by x.
     
  6. Nov 19, 2007 #5
    Alright, sure. Let's do it in steps.

    First, do:

    [tex] (1+x)^2 = (1+x)(1+x)[/tex]

    This should be quickly determined to be:

    [tex] 1+2x+x^2 [/tex]

    So, now note:

    [tex] (1+x)^3 = (1+x)(1+x)(1+x) = (1+2x+x^2)(1+x) [/tex]

    Then distribute:

    [tex] (1+2x+x^2)(1+x) = (1)(1+x) + (2x)(1+x) + (x^2)(1+x) = 1+x+2x+2x^2+x^2+x^3 [/tex]

    Then simplify:

    [tex] 1+x+2x+2x^2+x^2+x^3 = 1+3x+3x^2+x^3 [/tex]

    Now, remember your original expression and substitute:

    [tex] \frac{(1+x)^3-1}{x} = \frac{1+3x+3x^2+x^3-1}{x} = \frac{x^3+3x^2+3x}{x} = x^2+3x+3 [/tex]

    So, then, we have:

    [tex] \lim_{x\rightarrow 0} \left(\frac{(1+x)^3-1}{x}\right) = \lim_{x\rightarrow 0} \left(x^2+3x+3\right) [/tex]

    You can take it from here.
     
    Last edited: Nov 19, 2007
  7. Nov 20, 2007 #6
    thank you for clarifying that. Maybe i just needed a quick refresher to show me how again.
     
  8. Nov 21, 2007 #7
    Wait, so are you good? Or are you still confused?
     
  9. Nov 21, 2007 #8
    yes im good thank you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Rationalizing cubed expressions
  1. Rational Expression (Replies: 2)

  2. Rational Expressions (Replies: 3)

Loading...