Taylor polynomials associated with five common functions.
- Produce various graphs of Taylor polynomials
- Discover how the accuracy of a Taylor polynomial is associated with the degree of the Taylor polynomial
- Visualize the accuracy and relate this to symmetry, arc length, and a point of discontinuity
- Examine certain common functions and draw specific conclusions about the Taylor polynomial associated with these functions
- Taylor polynomial
- degree n
- accuracy of the approximation
- neighborhood of a
About the Lesson
This lesson involves Taylor polynomials associated with five common functions. As a result, students will:
- Learn about Taylor polynomials graphically and numerically.
- Conjecture about factors that affect the accuracy of Taylor polynomial approximations.
- Visualize the effects of n and a on the accuracy of the approximation.