Section 11.4 – Representing Functions with Power Series.

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Presentation transcript:

Section 11.4 – Representing Functions with Power Series

4.Find the power series representation for centered about x = 0 and specify its radius of convergence. Infinite geometric with first term 1/3 and r = -2x/3 Converges when |r| < 1

8. Find the power series representation for centered about x = 0 and specify its radius of convergence. Radius of Convergence is 1

12. Use the power series representation of power series representation of the function to produce a

18.Find a power series representation of f(x) = ln x centered at x = 1. Specify the radius of convergence of the power series. Radius of convergence is 1

26.Use an appropriate identity to find the Maclaurin series for f(x) = sin x cos x

30. Given the function f defined by a.Find the first three nonzero terms in the Maclaurin series for the function f.

30. Given the function f defined by b. Find the first three terms in the Maclaurin series for the function g defined by

30. Given the function f defined by b. Find the first four terms in the Maclaurin series for the function h defined by