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Bounded Function

  1. Sep 24, 2012 #1

    hsd

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    (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

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    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

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    2016 Award

    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.
     
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