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Derivatives of Vector Valued Functions and Tangent Vectors

Derivatives of Vector Valued Functions and Tangent Vectors
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2017-02-04 23:47
VectorFunctionCalculus
This example illustrates the derivatives of vector-valued functions and their tangent vectors in 3D space. Key mathematical concepts include vectors, derivatives, and functions. It utilizes commands such as CurveCartesian, Derivative, and Vector in GeoGebra. Suitable for university calculus courses.

GeoGebra Commands & Parameters

  1. CurveCartesian((cos(t), sin(t), (0.5 * t)), t, (-2 * π), (2 * π)) → r
  2. Derivative(r) → r'
  3. Vector(r'(t)) → u
  4. Vector(r(t), Point[r(t), u]) → v_{r'}
  5. Vector(r(t)) → v_{r}