Answer to Question #116788 in Calculus for Olivia

Question

The vector valued function r(t)=⟨t^3+4,e^t,cos(t)⟩

is
Select one:
a. continuous for all t∈R

b. only continuous for t∈[0,∞)


c. continuous for all t
except 0
d. only continuous at t=π


e. only continuous for t∈[1,∞)

Answer 1

Theorem. $r(t)=\big(f(t), g(t), h(t)\big)$ is continuous at $t=a$ if and only if all of $f, g, h$ are continuous at $t=a.$

$f(t)=t^3+4$ is continuous everywhere,

$g(t)=e^t$ is continuous everywhere,

$h(t)=\cos(t)$ is continuous everywhere.

The vector valued function $r(t)=\big(t^3+4, e^t, \cos(t)\big)$ is

a. continuous for all t∈R