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!

Proof that a function is continuous

  1. Jul 21, 2011 #1
    Prove that the function is continuous when f(x)=0
    f(x)=x4-7x3+11x2+7x-12


    f(c)-[itex]\epsilon[/itex]<f(x)<f(c)+[itex]\epsilon[/itex]

    Limits maybe taken, however, we do not have the value for c in the limit equation.
     
  2. jcsd
  3. Jul 21, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It looks like you have to solve for x, when f(x) = 0, i.e., find the zeros of f(x).

    For one of the zeros, notice that the sum of the coefficients of f(x) is zero. Therefore, f(1) = 0.

    So you know that one of the factors of f(x) is (x-1). Use long division or synthetic division to find g(x) such that: f(x) = (x-1)g(x).

    Added in Edit.
    Notice that: f(-x) = x4+7x3+11x2-7x-12. Therefore, f(-(1)) = 0 .
     
    Last edited: Jul 21, 2011
  4. Jul 21, 2011 #3
    Solving this gives (x-1)(x+1)(x-4)(x-3)
    But is this sufficient to show that it is continuous?
     
  5. Jul 21, 2011 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Of course not.

    The problem is to show that f(x) is continuous when f(x)=0. So the problem has become: show that f(x) is continuous for x = -1, 1, 3, 4 .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof that a function is continuous
Loading...