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Homework Help: Limit help

  1. Jan 18, 2006 #1
    Can someone point me in the right dirrection with this problem:

    find examples to show that if

    a) lim x->c [f(x)+g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

    b) lim x->c [f(x)*g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

    any help would be great
     
  2. jcsd
  3. Jan 18, 2006 #2

    HallsofIvy

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    Think simply: if f(x)= 1/x, what is the limit as x-> 0? what is limit of g(x)= -1/x as x-> 0? What about f(x)+ g(x)?
     
  4. Jan 18, 2006 #3
    would that still work for part B of the problem?
     
  5. Jan 18, 2006 #4
    Not that example because there is no limit of f(x)*g(x). Use the two examples of x^2 and 1/x^2
     
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