Taylor Series Explorer

Visualize Taylor and Maclaurin polynomial approximations with animation

Overview

The Taylor Series Explorer provides an interactive visualization of Taylor and Maclaurin series approximations. Watch polynomial approximations improve as you increase the degree, and explore how infinite series converge to represent complex functions using only polynomial terms.

Tips

  1. Use the animation feature to watch how the polynomial approximation gradually converges to the true function as you increase the degree
  2. Stay close to the center point for better accuracy - Taylor series work best near the point of expansion and may diverge far away
  3. Start with exponential and trig functions (e^x, sin, cos) which converge everywhere, then try ln(1+x) to see limited radius of convergence
  4. Compare different degrees to see how many terms you actually need for acceptable accuracy in your region of interest
  5. Note the alternating pattern in series like sin(x) and cos(x) - this helps explain why they work so well for approximation