Vector Functions: Show Limit as t Goes to a

[aesailor]

Homework Statement

Show that the lim r(t)=b as t goes to a if and only if for every \epsilon>0 there is a number \delta>0 such that |r(t) - b| < \epsilon whenever 0<|t-a|<\delta

Homework Equations

if r(t) = <f(t),g(t),h(t)>, then

limr(t) as t goes to a = <limf(t) as t goes to a, limg(t) as t goes to a, limh(t) as t goes to a>
I really have no idea on how to go about this problem

 

[tiny-tim]

haello aesailor!

(have a delta: δ and an epsilon: ε )

For each ε you have three δs …

but you need only one δ, so … ?

 

[aesailor]

I'm really confused by your response tiny tim

 

[tiny-tim]

For a particular ε, you have three δs (δ_f δ_g and δ_h, say) one for f, one for g, and one for h.

So the least of these will work for all three of f g and h.