We explore geometric series.  We create new power series from known ones by differentiation and integration.  The power series for e^x is explored.  We also write pi as an infinite series produced by integrating term by term of a problem producing an inverse tangent.

10.1 (BC only)  Power Series

AP Calculus lessons University High School Normal,IL

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Exploration of slopes of secant lines and tangent lines. The average and instantaneous rate of change is calculated with the difference quotient.
Day 1 is an independent activity  found here

http://www.uhigh.ilstu.edu/math/thompson/sketchpad/apcalc/2.4_The%20Leaning%20Tower%20of%20Pisa.doc

2.4 day 2

Euler's method to approximate the value of a function given a differential equation and initial point is explored.

Euler's Method (BC only)

We explore the integral test to determine convergence.  The harmonic series is revisited.

10.5 (BC only)  Integral Test for Convergence

We explore the comparison test and the ratio test to determine convergence.  The area inside polar functions is also explored as well as their slopes.

10.4 (BC only) Convergence and Polar functions

We explore the error bound for Taylor polynomials.

10.1 (BC only) Power Series

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