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What Do Functions Do for Tiny X?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

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Building Approximations for Sin(x)

Build up the concept of the Taylor series

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Taking Trigonometry Series-ly

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

Towards Maclaurin

Age 16 to 18 Challenge Level:

If you can show that the derivative of a function is always positive then the function is increasing and if you can show that the derivative is always negative then the function is decreasing.