post 36

This past week we took another AP test to get ready for the upcoming real AP test. Some old stuff to refresh some memories are as follows.

The steps for working linearization problems are:

1. Identify the equation

2. Use the formula f(x)+f ' (x)dx

3. Determine your dx in the problem

4. Then determine your x in the problem

5. Plug in everything you get

6. Solve the equation

The steps for related rates are:

1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation

e integration:very easy whatever e is raised to is your u, the derivative of u is du

The steps for substitution are:

1. Find u and du

2. set u equal to whatever isn't the derivative

3. take the derivative of u

4. substitute back in

The Riemann sum approximates the area using the rectangles or trapezoids. The Riemanns Sums are:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals