Taylor Polynomial Approximation
by Anonymous · ⭐ 0 · 🍴 0
The higher the degree, the tighter the polynomial hugs the curve. Overlay sin x, eˣ and 1/(1−x) from degree 0 to 6, move the center of expansion to see that it fits well nearby and drifts far away, then measure at one fixed point how fast the error shrinks.
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About this app
Taylor Polynomial Approximation is an interactive calculus visualizer for exploring how Taylor polynomials approximate sin x, eˣ, and 1/(1−x). Compare polynomial degrees from 0 through 6, move the expansion center to see how accuracy changes around x = 3, and measure approximation error at x = 0.5 with a visual error bar.
Use cases
- High school students studying Taylor series and polynomial approximation
- Teachers demonstrating how polynomial degree affects curve fitting
- Learners exploring the effect of changing the expansion center
- Calculus practice with approximation error and function comparisons
Features
- Interactive graphs of sin x, eˣ, and 1/(1−x)
- Taylor polynomial degree controls from 0 to 6
- Expansion-center control for comparing accuracy at x = 3
- Error measurement at x = 0.5 with a visual bar
- Guided missions covering degree, center, and error concepts