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: Bounded Function

  1. Sep 24, 2012 #1

    hsd

    User Avatar

    (a) Show that the function g(x) =[3 + sin(1/x-2)]/[1 + x^2] is bounded.
    This means to find real numbers m; M is an lR such that m ≤ g(x) ≤ M for
    all x is an lR (and to show that these inequalities are satisfied!).

    (b) Explain why the function:

    f(x) = { [x-2] [3 + sin(1/x-2)]/[1 + x^2] , if x ≠ 2,
    { 0 , if x = 2.

    is continuous at all x ≠ 2.

    (c) Show that the function f(x) in Part (b) is continuous at x = 2. [Hint: Use
    Part (a) and the Squeeze Theorem.]
     
    Last edited: Sep 24, 2012
  2. jcsd
  3. Sep 24, 2012 #2

    lanedance

    User Avatar
    Homework Helper

    how about considering g(x) = u(x)/v(x) and each of the behaviours of those functions

    note that g(x) will get big whenever u(x)>>v(x)
     
  4. Sep 25, 2012 #3

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF;
    How about showing us your attempt at the problem? ... that way we can target our assistance to where you need it most.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook