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Limit problem

  1. Sep 24, 2004 #1
    I'm stuck on one complicated limits problem, wondering if any of you could help me :) usually I am pretty fine with limits but this one uses all variables and has functions in it. Anyways, here it is:

    f(a) = b, g(b) = c, h(c) = d
    prove lim[x->a](h°g°f)(a) = d

    (° = "of")

    Can anyone help me?
  2. jcsd
  3. Sep 24, 2004 #2
    lim[x->a](h(g(f(x)))) = d eh?

    Well as x->a, f(x)->b
    let y = f(x)
    So now we have lim[y->b](h(g(y)))

    as y->b, g(y)->c

    Make sense? I guess the rest is obvious
  4. Sep 25, 2004 #3
    Thanks for your help, I just thought of something else, too. Seems like this works and is very easy, could you do just a quick check of it and see if it makes sense?

    f(a) = b, g(b) = c, h(c) = d

    lim[x->a](h(g(f(a)))) = d

    f(a) = b, so g(f(a)) = g(b)
    g(b) = c, so h(g(b)) = h(c)
    h(c) = d, which solves the problem
  5. Sep 25, 2004 #4
    Looks good to me. You may want to play it safe I'm not sure how meticulous your teacher expects you to me but I would accept that answer :)
  6. Sep 25, 2004 #5
    Thanks a bunch :)
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