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

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

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

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.

We explore the error bound for Taylor polynomials.

We explore creating Taylor polynomials. We also center them at other values and create new polynomials from given ones.

We explore creating Taylor polynomials. We also center them at other values and create new polynomials from given ones.

Work done pumping milk shake

Some example problems involving force and work. Lifting a leaky bucket and pumping to fill a tank.

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.