Taylor Polynomials Demo

Taylor Polynomials Demo
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2020-04-15 07:24
This example demonstrates how to dynamically visualize the approximation of a function by its Taylor polynomials using GeoGebra. It involves core mathematical concepts such as function approximation, polynomial functions, derivatives, and limits. Key GeoGebra commands and objects used include Sequence, Zip, Sum, Textfield, Simplify, along with f, n, a, Dfn, Dfneval, fapprox, A, InputBox1, text1, N, InputBox2, InputBox3, simpfn, text2. Suitable for high school students and above to learn and understand function approximation theory, as well as for calculus teaching demonstrations.

GeoGebra Commands & Parameters

  1. Sequence(Derivative[f, k], k, 0, n) → Dfn
  2. Zip(g(a), g, Dfn) → Dfneval
  3. Sum((Dfneval(k + 1) / k! * (x - a)^(k)), k, 0, n) → fapprox
  4. Textfield(f) → InputBox1
  5. Textfield(N) → InputBox2
  6. Textfield(a) → InputBox3
  7. Simplify(fapprox) → simpfn