AP Calculus

Going over the 9/11/06 homework

• For whether the rate of change is slow or fast: is based on the steepness of the graph. For example if the graph is increasing and the slope is steep then the rate of change is fast. If the slope is not very steep then the rate of change is slow. This applies for whichever direction the graph is going whether it is increasing or decreasing.
• Secant is the reciprocal of Cosign. 1/cosign=secant.
• Secant and the inverse of cosign is different. Y=cos^-1 is the same as saying Cos y=x. Inverse is switching the domain and range.
• Decreasing means negative and Increasing means positive. For example: Decreasing at about 9.95 ft/sec means that the average rate for that problem was (-9.95).

Class Notes

Intro to Derivative and Limit:

• Derivative: the instantaneous rate of change at a particular point.
• Example: find the derivative at .3, means find the slope of the function at that point. Because its slope at a particular point and not between two points it is an instantaneous rate of change.
• Limit: L is the limit of F(x) as x approaches c iff (if and only if) L is one number you can keep f(x) arbitrarily close to just by keeping x close enough to c, but not equal to c.
• For example: y=x^2. What is the limit of x^2 as x approaches 3. The limit is equal to 9. The limit is the y. Only if you can always find an x value on either side of three that is a close to three as you can get.
• Two Branches of Calculus: Differential= Study of derivatives. Integral: Study of integrals.

Homework: pg 12 in textbook. Do problem set 1-2 Q’s in your head. 11-27 ODDS! Due Friday 9/15. Read Section 1-3.

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