** 25.T Taylor
expansions** (<-READ ME)

** Reference: ** Stewart 2.9 (review, emphasis on quadratic
approximations), 10.10 (ignore infinite sums for now), 10.11,
CalcLabs 10.5

** Keywords: ** Taylor polynomial,
Taylor expansion or series, Maclaurin expansion or series,
geometric series, binomial series

** Learning Objectives: ** The student will be able to:

- Compute Taylor polynomials, of a given degree
*n*, about a given point*a*, for a given function*f* - Know and use the Maclaurin series of exp, sin, and cos, and the geometric series
- Use Maple's
**taylor**command to find Taylor polynomials - Use Maple to plot graphs of functions and their Taylor polynomials

** 25.R
Mean value theorem, Taylor's theorem **(<-READ ME)

** Reference: ** Stewart 3.2, 10.9, 10.12 (ignore infinite sums for
now)

** Keywords: ** Rolle's theorem, mean value theorem (MVT),
Taylor series, Taylor's theorem with remainder,
error term, perturbation theory

** Learning Objectives: ** The student will be able to:

- State Rolle's Theorem and the Mean Value Theorem
- Verify whether or not a given function satisfies the hypotheses of the MVT
- State Taylor's formula with remainder
- Use the remainder to estimate the error when using Taylor polynomials
- Use Taylor polynomials in applications