1. Limited time only! Sign up for a free 30min personal 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!

Limit question, evalute for C

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data

    lim [itex]\frac{\sqrt[3]{1+cx}-1}{x}[/itex]

    3. The attempt at a solution

    I put 0 in for x, which lead to 0/0 therefore I know I know I need to modify to get a real answer. I have no idea where to start.
  2. jcsd
  3. Feb 20, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Are you allowed to use L'Hôpital's rule ?

    If not, then rationalize the numerator.

    a3 - b3 = (a - b)(a2+ab+b2)

    So that [itex]\displaystyle \ \ (\sqrt[3]{s}-\sqrt[3]{t})((\sqrt[3]{s})^2+\sqrt[3]{s}\sqrt[3]{t}+(\sqrt[3]{t})^2)=s-t[/itex]
  4. Feb 20, 2013 #3
    So it's like multiply by a conjugate for square root rationals, but for a cube root??

    Equivalent to x^2-y^2=(x-y)(x+y) ???
  5. Feb 20, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Do you know about Taylor series? If so, just take the first few terms of the expansion of ##(1+cx)^{1/3}## about ##x=0##.
  6. Feb 20, 2013 #5


    User Avatar
    Science Advisor

    Yes, but x^3- y^3= (x- y)(x^2+ xy+ y^2).
  7. Feb 20, 2013 #6
    or you can use the limit:

    [itex]\displaystyle\lim_{\begin{matrix}f(x)\to 0\\\mbox{when }x\to x_0\end{matrix}}\frac{(1+f(x))^\alpha-1}{f(x)}= \alpha\qquad (\heartsuit)[/itex]

    You have just to multiply and divide by [itex]c\ne 0[/itex] and use [itex](\heartsuit)[/itex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Limit question, evalute for C
  1. Evalution of a Limit (Replies: 3)

  2. Evalutating integerals (Replies: 3)

  3. Limits question (Replies: 6)

  4. Limit question (Replies: 3)

  5. Limits question (Replies: 5)