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Sec. 11.1: Vector-Valued Functions and Space Curves

Sec. 11.1: Vector-Valued Functions and Space Curves. Definition: Let D be a set of real numbers. A vector-valued function r with domain D is a correspondence that assigns to each number t in D exactly one vector r ( t ) in V 3 . Note : From now on we will consider r ( t ) a

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Sec. 11.1: Vector-Valued Functions and Space Curves

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  1. Sec. 11.1: Vector-Valued Functions and Space Curves Definition: Let D be a set of real numbers. A vector-valued function r with domain D is a correspondence that assigns to each number t in D exactly one vector r(t) in V3. Note: From now on we will consider r(t) a position vector, and we will refer to the terminal point of r(t) as its endpoint.

  2. Example Click for Answer Cool 3-D Vector-Valued Function Grapher

  3. In general the endpoints of a vector-valued function determine a space curve, or just a curve. • The components of the vector-valued function are parametric equations for the curve C. • The orientation of C is the direction determined by increasing values of t.

  4. Smooth Curves

  5. A Twisted Cubic

  6. Circular Helix

  7. Example 2-D Vector-Value Function Grapher

  8. Arc Length

  9. Example

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