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Main Limit Theorem

  1. Jan 21, 2009 #1
    My teacher told me it was best to learn in words. can anyone help me with the correct why to write these.

    Let n be positive interger, K be a constant, and f and g be function that have limits at C. then

    1. lim k = k
    x-> c
    2. lim x= c
    x-> c
    3. lim kf(x) = k lim f(x)
    x-> c x-> c
    4. lim [ f(x) + g(x)] = lim f(x) + lim g(x)
    x-> c x-> c x-> c
    5. lim [ f(x) - g(x)] = lim f(x) - lim g(x)
    x-> c x-> c x-> c
    6. lim [ f(x) * g(x)] = lim f(x) * lim g(x)
    x-> c x-> c x-> c
    7. lim f(x) = lim f(x) provided that lim g(x) does not equal 0
    g(x) x-> c
    lim g(x)
    x-> c
    8.lim [ f(x)]n = [ lim f(x)]n
    x-> c x-> c
    9.lim n radical f(x)= 2radical f(x), provided lim f(x) is less then 0
    x-> c x-> c
    when n is even

    for example in the book they mention no. 4 as the limit of a sum is the sum of the limits. so can anyone else help me out with the others?
     
  2. jcsd
  3. Jan 21, 2009 #2
    1) The limit of a constant is the constant itself.

    2) The limit of a variable is the limit the variable is taken to.

    3) Scalars can always be pulled out of the limit.

    5) The same thing as #4 since subtraction is just the sum of the negative.

    6) The limit of the product of multiple functions is the product of limits of each function (aka The limit of the product of two functions is the product of the limits of each of the two functions)

    Etc..
     
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