A Maclaurin series is a power series

which provides an approximation for y near x=0.

It is a way of “coding” functions into a standard form, i.e. power series.

It doesn’t work for all functions, but it does work for a lot of them.

The coefficient can be calculated from

For many functions the approximation can be made as good as you like, or even as good as you like for x as big as you like, by calculating enough terms of the power series.

Maclaurin series can be used

- to find approximate solutions to differential equations which can’t be solved otherwise
- to calculate values of functions like for different values of x
- to make it easier to differentiate functions
- to make it possible to integrate functions which can’t be integrated otherwise.

Click here for pdf on Maclaurin series

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