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!

Homework Help: Different Way to Solve a Limit of an Indeterminate Equation

  1. Aug 14, 2008 #1
    lim_{x\rightarrow-2}\frac{x^3 + 8}{x+2}

    Ok, I have solved this using synthetic division in which the limit was 12, however I was wondering if there was a way to solve this without using synthetic division (seeing as I hate the process of it).

    I've solved plenty of other indeterminate equations by factoring out a polynomial and then being able to cancel out so that I can then plug in x, but I wasn't able to do so with this one.

    I'm just curious if there are any other ways to solve this specific limit.

  2. jcsd
  3. Aug 14, 2008 #2
    L'hospital rule (applies only when it is in forms like 0/0, inf/inf)

    differentiate both num and den, and then sub in your -2
  4. Aug 14, 2008 #3
    Yeah I started reading up on that rule, but didn't understand it fully until your reply. So the derivative of the numerator is 3x^2 and the denominator is 1 so then just sub in the -2 and you get 12. Got it, thanks a lot for clearing up that rule for me.
  5. Aug 14, 2008 #4


    User Avatar
    Homework Helper

    Not that this is much different than using synthetic division, but the numerator is a sum of two cubes, which factors according to

    [tex]a^3 + b^3 = (a + b) \cdot (a^2 - ab + b^2)[/tex] . So, in fact, this numerator can be factored and the (x + 2) term can be cancelled.
    Last edited: Aug 14, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook