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Homework Help: Limit homework problem help

  1. Mar 1, 2007 #1
    1. The problem statement, all variables and given/known data
    f(x) is a piecewise function defined as:

    [tex]2(2e-e^x) x<1[/tex]
    [tex]3\pi x-4 x>=1[/tex]

    Discuss the continuity of f(x) at x=1.


    2. Relevant equations



    3. The attempt at a solution

    Putting x=1 in the above function gives you 2e and [tex]3\pi -4[/tex]. They seem to be equal, but how do I prove it mathematically? I've missed something here, but dont know what.
     
  2. jcsd
  3. Mar 1, 2007 #2

    Dick

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    How many decimal places are you looking at? They aren't THAT close to being equal.
     
  4. Mar 1, 2007 #3
    No idea. Is this thing continuous at x=1?
     
  5. Mar 1, 2007 #4

    Dick

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    It's a lot easier to show they aren't equal than that they are. Hint: they can't be equal, e and pi are algebraically independent. Just punch the things into calculator that shows more than two decimal places.
     
    Last edited: Mar 1, 2007
  6. Mar 4, 2007 #5
    Yeah, I did just that. The question has other parts which can only be solved if this thing was continuous. Nasty assumption.
     
  7. Mar 5, 2007 #6

    HallsofIvy

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    2e and 3[itex]\pi[/itex]-4 are definitely NOT equal!
     
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