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Math Help - Calculus III But doesn't require Calculus :)

  1. #1
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    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 ..."?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by 1005 View Post
    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"
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