11.1 – Polynomial Approximations of Functions

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Presentation transcript:

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

Find the local linearization of

Find the Taylor Polynomial

Find the Taylor Polynomial

This means x = 0.

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

Find the third degree Taylor polynomial for

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

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

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)

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.