1/22

Today we talked more about definite integrals and the Fundamental Theorem of Calculus

Integral Ideas

 

1/23

Today we continued to look at the idea of the definite integral and investigating areas underneath curves. 

ONE MAJOR IDEA: If the area is above the x-axis, the area is a positive value. If the area is below the x-axis it is negative!

Be careful when combining areas on both sides

1/14 

Integration Ideas and Riemann Sums

3 Khan's: Accumulation, Left and Right Riemann Sums, Midpoint and Trapezoid Sums

 

1/15

Today we found other ways of estimating area: trapezoid sums and midpoint sums

Notes

1 Khan: Trapezoid and Midpoint

 

1/16

Today we started to investigate how to write riemann sums in summation notation

Notes

 

1/18

Summation Notation Riemann Sums simplified

1/4

Today we talked about linear approximation. Aka using a nearby known point and slope to find the approximate value of a curvy function using a straight line.

Notes

Khan: Linear Approximation

 

1/7/19

Today we introduced optimization. These questions delt with finding minimum requirements to meet certain area or volume needs. 

Optimization 1

Examples to try:

1. You are designing a cylindrical tube that must hold 1000 cm cubed of volume. If the cylindar has an open top, what is the minimum surface area required to create the cylinder?

 

1/8/19

Today we continued optimization

Opt. 2

no hw

 

 

1/11/19

Optimization 3

1 Khan Optimization