# Thread: Calculus III But doesn't require Calculus :)

1. ## Calculus III But doesn't require Calculus :)

For my calculus III class, we began with elementary study of three dimensional vector equations.

One exercise asks for the domain of r(t) = e^(t)i + t(-1)j + (t+1)^(-3)k
I know the answer is t ≠ 0 or -1. However, when I looked the answer up, it was given like so: D = {t ∈ R, t ≠ 0, t≠ -1}

What does t ∈ R do? Specifically, what is ∈? Because I know t is a parametrized variable and R refers to the function of those parts.

Does it mean "for whenever R is parametrized with t, the domain is ..."?

2. Originally Posted by 1005
For my calculus III class, we began with elementary study of three dimensional vector equations.

One exercise asks for the domain of r(t) = e^(t)i + t(-1)j + (t+1)^(-3)k
I know the answer is t ≠ 0 or -1. However, when I looked the answer up, it was given like so: D = {t ∈ R, t ≠ 0, t≠ -1}

What does t ∈ R do? Specifically, what is ∈? Because I know t is a parametrized variable and R refers to the function of those parts.

Does it mean "for whenever R is parametrized with t, the domain is ..."?
$\mathbb{R}$ denotes the set of real numbers.

$\in$ denotes "belongs to", "is a member of", "is an element of" etc

so saying $t \in \mathbb{R}$ is the same as saying, $t$ is a real number, or belongs to the set of real numbers.

thus, the domain as given says "the domain is the set of all real numbers that are not equal to 0 or -1"