Lesson #32
Parametric Equations




Quote of the Day:
"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya

Objectives:
The student will learn to take derivatives of parametric equations.

The student will prove the quotient rule for derivatives.



1. Collect Homework.

2. Prove the Quotient Rule (using the Chain Rule)



3. Pattern Problem:

The pattern AABBBCCCCAABBBCCCC... continuously repeats.
What is the 2003rd letter in the pattern?

Solution: B

The cycle AABBBCCCC consists of 9 letters, so the final C in the pattern occurs as letter number 9, 18, 27, 36, and so on.

Since 2003 = 9 (222) + 5, the 2003rd letter is the 5th letter in the cycle, B.

This is from a branch of mathematics known as modular arithmetic.
Those of you taking C++ Programming recognize the mod function.

4. Review: Determine the 80th derivative of y = cos(2x)



5. Parametric Equations





6. Assignment:
p. 216 (66, 68) -- in class?
p. 208 (36)
p. 93 ( 1, 3, 5, 6)
Droodle Review Worksheet

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Send any comments or questions to: David Pleacher