Vector-Valued Function

  • #1

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)] >
 

Answers and Replies

  • #2
LCKurtz
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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))##?
 

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