Randolph H.S. AP Calculus AB '09: January 2010

Wednesday, January 27, 2010

Differential Equations, Initial Value Problems

Below are the problems we worked on in class today. They are from Larson 7.0 Chapter 4 Section 1

The problems below are similar to those above. They are initial value word problems. Please complete them for tomorrow.

Monday, January 25, 2010

Indefinite Integration and Anti-Differentiation

Below are the problems we worked on today. They are in Larson 7.0 Chapter 4 Section 1. Please be work through all of the odd problems tonight. Thank you!

Tuesday, January 19, 2010

Midterm

In addition to limits, you should know the following:

From the Calc A class:
1. Implicit differentiation (has horizontal tangents when the numerator is zero, vertical tangents when the denominator is zero)
2. Find equations of tangent lines and normal lines (normal line is perpendicular to the tangent line at the point of tangency)
3. Derivatives of exponential and logarithmic functions
4. Don't forget the chain rule, the product rule, the quotient rule!
5. Remember how to show that something is differentiable - limit must exist, must be continuous and slopes from the left and right must agree.
6. A function has a horizontal tangent when its derivative is 0. Set the derivative equal to zero and solve for x.
7. Remember limits as x approaches infinity are the same as horizontal asymptotes.

Also:
Related rates
Optimization
Increasing/Decreasing/Relative Extrema
Concavity/Points of Inflection
Motion Problems

Good luck!

Monday, January 18, 2010

Midterm Review

Below is a beginning of the midterm review. The first is on limits.

Limits Review

There are 8 videos that go with the limit review:

Limits overview (part 1)
Limits overview (part 2)
Limits overview (part 3)
Limits algebraically
Infinite limits (the behavior of a function around a vertical asymptote)
Limits at infinity (part 1)
Limits at infinity (part 2)
Limits of trig functions

More to follow!

Wednesday, January 13, 2010

Basic Differentiation Rules

Note that "u" in the above formulas refers to a function of "x" and hence implies the chain rule. "u'" is the derivative of "u" with respect to "x", or "du/dx".

I have also included the previous charts on EVT, MVT, and Rolles Theorem, as well as basic concepts and definitions. You should know that a critical value is where f'(x)=0 or DNE, and that relative extrema always occur at critical values, but a critical value does not guarantee the existence of relative extrema, as in f(x)=x^3 at x=0.