Power Series

Power Series

Definition of Power Series

Maple Worksheet on graphing functions defined by power series using finite series approximations

Example 1

Determine the domain of the given function defined by a power series.

Graph of the Function

Example 2

Convert the given function to a power series representation with a restricted domain.

Graph of the Function

Example 3

Determine the interval of convergence of the power series defining f(x). This would also give us the domain of the function.

The graph of the function is approximated below by graphing

over the interval [-2.99,2.99].

The graph is pretty accurate.

Example 4

Determine the interval of convergence of the power series defining f(x). This would also give us the domain of the function.

The graph of the function defined by the power series is shown above. What is the name of this function?

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu