10.11 Finding Taylor Polynomial Approximations of Functions
- Syllabus
- 2020
- Topic
- 10.11
- Level
- —
LIM-8.A—Represent a function at a point as a Taylor polynomial
- LIM-8.A Represent a function at a point as a Taylor polynomial.
- LIM-8.A.1 The coefficient of the nth degree term in a Taylor polynomial for a function f centered at x = a is f⁽ⁿ⁾(a)/n!.
- LIM-8.A.2 In many cases, as the degree of a Taylor polynomial increases, the nth degree polynomial will approach the original function over some interval.
- Enduring understanding LIM-8: Power series allow us to represent associated functions on an appropriate interval.
LIM-8.B—Approximate function values using a Taylor polynomial
- LIM-8.B Approximate function values using a Taylor polynomial.
- LIM-8.B.1 Taylor polynomials for a function f centered at x = a can be used to approximate function values of f near x = a.
- Enduring understanding LIM-8: Power series allow us to represent associated functions on an appropriate interval.
Objective notes
2 learning objectivesConceptAP Calculus BC