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Theorem of continuity and limits converge

  1. Nov 18, 2007 #1
    1. The problem statement, all variables and given/known data
    If lim x--> a of [f(x) + g(x)]=2 and lim x--> a of [f(x) - g(x)] = 1, then find lim x--> a f(x)g(x)


    2. Relevant equations
    Theorems of continuity


    3. The attempt at a solution
    Since i'm not quite sure if what I began with was right, it didn't yield me any type of a valid answer. But from the theorems of continuity (lim x--> a of f(x)=f(a)), I began with saying lim x-->2 of [f(x)+g(x)]=2 and lim x-->1 of [f(x)-g(x)]=1

    is that a good place to start? where do I go from here?
    thanks
     
  2. jcsd
  3. Nov 18, 2007 #2

    Dick

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    You mean continuity of f and g tells you f(a)+g(a)=2 and f(a)-g(a)=1, right? That's two equations in two unknowns. You should be able to solve for f(a) and g(a).
     
  4. Nov 18, 2007 #3
    right, i've figured that part
    i was wondering where I begin doing that?

    thanks
     
  5. Nov 18, 2007 #4

    Dick

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    Add the two equations together to get an equation for just f(a).
     
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