Derivative of vector-valued function
Tangent vector as a limit
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Quicktime format
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Animation to illustrate the limiting process involved in the definition of the derivative: control h using the slider
The tangent vector at the point
The derivative gives a tangent vector
Tangent vectors from the derivative
The derivative of the elliptical helix as another vector-valued function.
Arc length
Arc length animation (BIGGGG...)
Approximating arc length on a helix-like curve
Arc length animation
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Quicktime format
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Same animation as above with control of delta t using the slider
Derivative of a curve that sweeps out a trefoil knot
Animation to illustrate the speed at which a point traverses a curve