Does the Limit of a Sum Equal the Sum of the Limits for Vector-Valued Functions?

[voodoochild]

Homework Statement

Let r (t)=f(t),g(t),h(t)and s(t)=〈F(t),G(t),H(t)〉.
Show that lim(t→a)(r (t)+s (t))=lim(t→a)[r (t)]+lim(t→a)[s (t)].

Homework Equations

The Attempt at a Solution

I know that if a function r = <f,g,h> and lim(t→a)[r(t)] then lim(t→a)[r(t)] = < lim(t→a)[f(t)], lim(t→a)[g(t)], lim(t→a)[h(t)] >

 

[LCKurtz]

Homework Statement

Let r (t)=f(t),g(t),h(t)and s(t)=〈F(t),G(t),H(t)〉.
Show that lim(t→a)(r (t)+s (t))=lim(t→a)[r (t)]+lim(t→a)[s (t)].

Homework Equations

The Attempt at a Solution

I know that if a function r = <f,g,h> and lim(t→a)[r(t)] then lim(t→a)[r(t)] = < lim(t→a)[f(t)], lim(t→a)[g(t)], lim(t→a)[h(t)] >

OK, so what happens if you apply that last statement to $\lim_{t\to a}(r(t)+s(t))$?