# Calculus III But doesn't require Calculus :)

• Jun 19th 2009, 05:14 PM
1005
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 ..."?
• Jun 19th 2009, 05:23 PM
Jhevon
Quote:

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"