Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to rewrite limit to prove?

  1. Feb 10, 2008 #1
    I'm taking calculus I in college right now and for some reason we stated with limits...We're giving the following limit (sorry, I don't know how to work the board's code to make it look pretty):

    lim (x->3) is (x+6) / (x^4 - 4x^3 + x^2 + x + 6) = -1

    The prof suggested we rewrite lim (x->3) is (x+6) / (x^4 - 4x^3 + x^2 + x + 6) + 1 = 0 in the form (x-3)g(x) and find g(x). Any idea what g(x) would be and how to find it?
  2. jcsd
  3. Feb 10, 2008 #2
    Did you ever think about just plugging in 3 for x and seeing what happens?
  4. Feb 10, 2008 #3
    Yep, I did. I get -1 = -1. But considering it's a class exercise and the prof wants us to rewrite it as (x-3)g(x) I'm clueless...
  5. Feb 10, 2008 #4


    User Avatar
    Science Advisor

    so do the algebra! What is
    [tex]\frac{x+6}{x^4- 4x^3+ x^2+ x+ 6}+ 1[/tex]?

    I assume you know that is the same as
    [tex]\frac{x+6}{x^4- 4x^3+ x^2+ x+ 6}+ \frac{x^4- 4x^3+ x^2+ x+ 6}{x^4- 4x^3+ x^2+ x+ 6}[/tex]

    Add and try to factor the numerator. If you already know one factor, that should be easy!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook