Taylor Polynomial Approximation
by Anonymous
Raise the degree and shift the center of expansion to see how closely the Taylor polynomial hugs the curve and how fast the error shrinks.
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About this app
Taylor Polynomial Approximation is an interactive calculus learning app that visualizes how Taylor polynomials approach the curves of sin x, eˣ, and 1/(1−x). Explore the effects of changing the polynomial degree, moving the expansion center, and measuring approximation error at x = 0.5.
Use cases
- High school and introductory calculus students studying Taylor approximations
- Teachers demonstrating polynomial approximation with visual graphs
- Learners comparing approximations for common functions
- Students investigating how expansion centers affect accuracy
Features
- Interactive graphs comparing the actual function curve with its Taylor polynomial
- Degree controls ranging from 0 to 6
- Selectable functions: sin x, eˣ, and 1/(1−x)
- Expansion-center exploration using a target point at x = 3
- Error visualization at x = 0.5 with an error bar
- Guided missions covering degree, center, and error concepts