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Can i slit up lims

  1. Apr 11, 2009 #1
    if i have a lim of f(x)*g(x) can i say it is limf(x)*limg(x) like i could if i had lim of f(x)+g(x),
    more specifically, in my homework i have a question where,

    lim f(x) converges

    lim g(x) diverges

    and i am asked about convergence of lim u(x) when
    1) u(x)=f(x)+g(x)
    2) u(x)=f(x)*g(x)

    for 1) i say
    lim f(x)+g(x)= lim f(x) + lim g(x)====> diverges

    for 2) im not sure, but i think
    if f(X) converges to any number, K*inf=inf and u(x) diverges
    if f(X) converges to 0 , then 0*inf is undefined and u(x) diverges

    1st of all i am not 100% that i am right, second of all how do i prove this MATHEMATICALLY?
  2. jcsd
  3. Apr 11, 2009 #2


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    Hi Dell! :smile:

    (have an infinity: ∞ :wink:)

    Hint: x -> ∞ for f(x) = 1/x2, g(x) = x3 ?

    x -> ∞ for f(x) = 1/x2, g(x) = x ? :wink:
  4. Apr 11, 2009 #3
    in that case it really does diverge, but can i do that, just take any 2 functions and see what happens with them?? surely that is just one example and not enough to prove anything
  5. Apr 11, 2009 #4
    o i see what you are saying, you are DISPROVING what i said,
    so what does this mean? tha nothing can be said about fx*gx?? was i right about fx+gx??
  6. Apr 11, 2009 #5


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    Yes and yes :wink:
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