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Homework Help: Calculus: Limits

  1. Jun 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Given that
    lim f(x) = -4 and lim g(x) = 6
    (All limits x --> +infinity)

    Find the limit
    lim [f(x) + 2g(x)]

    2. Relevant equations

    3. The attempt at a solution
    So I substituted the values of f(x) and g(x) in the equation

    =[(-4) + 2(6)
    the limit is = 8

    Did I do it right?
  2. jcsd
  3. Jun 28, 2015 #2


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  4. Jun 28, 2015 #3
    Thanks! It was a wiley assignment and I thought I did it wrong xD
  5. Jun 28, 2015 #4


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    What else could the limit possibly be?
  6. Jun 28, 2015 #5
    Sorry! I was just making sure.
  7. Jun 28, 2015 #6


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    You should know from basic properties of limits that
    1) For any constant A, as long as lim f(x) exists, then so does lim Af(x) and the limit is A(lim f(x)).
    2) As long as lim f(x) and lim g(x) exist, then so does lim f(x)+ g(x) and the limit is lim f(x)+ lim g(x).

    Those two together give the result you want.
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