Homework Help: Limit problem variables

1. Sep 24, 2004

Hygelac

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. Sep 24, 2004

vsage

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

3. Sep 25, 2004

Hygelac

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

4. Sep 25, 2004

vsage

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 :)

5. Sep 25, 2004

Hygelac

Thanks a bunch :)