1. 11.1 – Polynomial Approximations of Functions
Taylor Polynomial of a function at x = c

2. Find the local linearization of

3. Find the Taylor Polynomial

4. Find the Taylor Polynomial

8. This means x = 0.

11. Find a third-degree Maclaurin polynomial that has the given
values for the function f and its derivatives at x = 0 and use
it to approximate f(0.2)
f(0) = 1, f ’(0) = -2, f ’’(0) = 8 and f ’’’(x) = -24

12. Find the third degree Taylor polynomial for

13. 20. If cos x is replaced by
estimate the maximum error by graphing

14. 22. Consider the function that satisfies
and contains
(1, 1). The solution of this can be approximated by using
Taylor polynomials.
a. Write the fifth degree Taylor polynomial for f at x = 1

15. 22. Consider the function that satisfies
and contains
(1, 1). The solution of this can be approximated by using
Taylor polynomials.
b. Estimate the value of f(1.75)

16. c) Verify that the function f(x) = xln x – x + 2 satisfies the dif. eq.
Use this function to find f(1.75) and compare with part b.