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Towards Maclaurin

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

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Taking Trigonometry Series-ly

Look at the advanced way of viewing sin and cos through their power series.

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Bessel's Equation

Get further into power series using the fascinating Bessel's equation.

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem begins to motivate the existence of the Maclaurin's series in which any function which is well-behaved at the origin can be written as an 'infinite polynomial' or 'power series'. This iterative method is a numerical way of finding the coefficients of the polynomial, although calculus can be used in cases where the derivatives of the function needing to be approximated are known.