Taylor Polynomial


Simple Taylor Polynomial approximation to a function. Enter a function in the green entry box. Move the orange plus symbol on the x-axis for the central point of the expansion. Move the slider to change the order of the approximation (number of terms) What happens near the expansion point as the number of terms is increased? What happens far away from the expansion point as the number of terms increases? Function suggestions:
  • x^2 + 4x + 1
  • sin(x)
  • exp(x)
  • atan(x)
  • sqrt(x)
  • tan(x)
  • nroot(x,3)
Take special note of the radius of convergence where the expansion point, , is close to 0 for the square-root and cube-root functions. Another interesting set of expansion points is points near .