|SimReal: Mathematics - Differentiation - Vector|
This application visualizes the derivative of a vector.
By default we have a vector sliding on the graph of the function:
y = f(x) = 8-0.05(x-5)2
This curve is parameterized by the parameter t = 0.25x (can be changed).
We want to study the derivative dr/dt of the vector to the point A on the graph.
Mark the checkbox ΔrA to show the vector to point A
Mark the checkbox ΔrB to show the vector to point B
Mark the checkbox Δr to show the difference vector ΔrB - ΔrA
Mark the checkbox Δr/Δt to show the vector Δr divided by Δt
Mark the checkbox 'dr/dt' to show the derivative of the vector ΔrA
Use the scrollbar at the bottom of the simulation window
to move the point B closer and closer to point A.
Look how Dr/Dt comes closer and closer to the dr/dt.
Control objects : Scrollbar : Move the point B on the graph xA : Left endpoint A xB : Right endpoint B Parameterization : Parameterization of the function rA : Show the vector to the point A rB : Show the vector to the point B Δr : Show the difference vector rB-rA Δr/Δt : Show the difference vector divided by Dt dr/dt : Show the derivative of the vector rA Tangent : Show the tangent line at point A Point : Show the end points A and B Axis : Show axis Grid : Show grid Graph : Show the graph of the function Formula : Show the formula for derivate of the vector rA Frm : Show a part of the formula (together with simulation window) Reset : Reset the application