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Homework Help: Limits and Continuity

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Postal charges are $.25 for the first ounce and $.20 for each additional ounce or fraction thereof. Let c be the cost function for mailing a letter weighing w ounces.
    a) Is c a continuous function? What is the domain?
    b) What is c(1.9)? c(2.01)? c(2.89)?
    c) Graph the function c.


    2. Relevant equations



    3. The attempt at a solution
    For a I got:
    No. The domain is all real numbers > 0.
    B is where I get stuck, I understand the question it's just I cant get what the integer function would be..
    C I could do once I have b..
     
  2. jcsd
  3. Sep 25, 2011 #2

    SammyS

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    Re: Limits/Continuity

    Can you answer B simply by applying what is stated, without resorting to some sort of mathematical "formula" ?
     
  4. Sep 25, 2011 #3
    Re: Limits/Continuity

    I guess I can answer b, but then how would I graph the function for part c :|

    edit: I see what you are getting it, I think I can make a graph too, thanks lol :p
     
  5. Sep 25, 2011 #4
    Re: Limits/Continuity

    Well I got the answers, but for my own knowledge can you tell me what this function would actually be?
     
  6. Sep 25, 2011 #5

    SammyS

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    Re: Limits/Continuity

    Are you referring to the Greatest Integer function when you say "the integer function" ?

    There are many integer functions. Two common ones are the "floor" function (a.k.a. Greatest Integer function), and the "ceiling" function.
     
  7. Sep 25, 2011 #6
    Re: Limits/Continuity

    Yep ment greatest integer function, I'm pretty sure it's applied here since it says: $.20 for each additional ounce or fraction thereof
     
  8. Sep 25, 2011 #7

    SammyS

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    Re: Limits/Continuity

    Greatest Integer function, a.k.a. floor function
    floor(x) = the greatest integer that's less than or equal to x .

    Doesn't work: floor(1.9) = 1

    floor(x) + 1 is close, floor(1.9) + 1 = 2 ---- but floor(1) + 1 = 2, not 1 .
    Try -floor(-x):
    -floor(-(1.9)) = - (-2) = 2 , OK

    -floor(-(1)) = - (-1) = 1 , OK
     
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