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Help with multivariate Calculus

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that:

    max{a,b}=1/2*(a+b+|a-b|)

    Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)}
    is also continuos.

    Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set g(x) = f(x+1-f(x). Prove that g(x) ---->0 and x----> inf.


    3. The attempt at a solution

    How do I start attempting such questions? I am thinking of taking multivariate next sem and am wanting to prepare myself for such questions....

    Thank you
     
  2. jcsd
  3. Feb 18, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi am100181! Welcome to PF! :wink:

    Just treat the two cases a≥ b and a< b separately. :smile:
     
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