Calculus/ 3rd six wks/ Assignmnets

1.Derivatives of Trig functions- Section 3.8/ pg. 170/ #1-6 all & #9-12 all (turned in)
2.Extrema- Global and Local- Packet/ #1-12 all (turned in)
3.Extrema- Global and Local- Packet/ #20-24 all and 32, 34 (turned in)

4.Extrema- Global and Local- Packet/ #36-40 all, Any 2 from 41 thru 45, #1, #2
5.Test take-home/ Problems with f f' f'' (Due Monday 12-14-09)
6.Mean Value Theorem- Packet/ #1-12 all ( did not complete)
7.Test take-home/ Over view of topics for fall semester

Sec.3-8 Deriv of Inverse trig functions- Solutions

Section 3-8/ Pg. 170/#1-6 all & 9-12 all

Here is step by step solutions to most of the home work problems. We can not go over it tomorrow in class- but I will be tutoring at 7:50 am.

Project Due on Monday after Thanks-Giving

1) Choose from one of the topics
*Connections between Math and the Arts
*Fibonacci sequence
*Golden Ratio
*Imaginary and Complex Numbers
*Artists that use Math
*Mathematicians that use Art
*transcendental Numbers
*Music and Math
*Any calculus topic

2) Decide How to present your project: Choose from the following:
*Make it online on your blog.
*Make it digital = multimedia, video, music composition…etc
*Make something physical, a 2-D or 3-D visual object, such as a collage, a painting or a mobile, sculpture...etc

The wonderful debate in our last class...

Below is Rae's math sing along. Royce's and Rae's methods are both correct. The issue was due to the mistake on the board. Watch this clip and see if you can find the mistake :)
And by the way, thank you for making Calculus a blast!

Chain Rule Examples

Interactive practice- click here

Example 1: Find the derivative f '(x), if f is given by
f(x) = 4 cos (5x - 2)
Solution to Example 1
Let u = 5x - 2 and y = 4 cos u, hence du / dx = 5 and dy / du = -4 sin u
We now use the chain rule f '(x) = (dy / du) (du / dx) = - 4 sin (u) (5)
We now substitute u = 5x - 2 in sin (u) above to obtain f '(x) = - 20 sin (5x - 2)

Example 2:
Find the first derivative of f if f is given by
f(x) = sin 2 (2x + 3)
Solution to Example 2
Let u = sin (2x + 3) and y = u 2 , hence du / dx = 2 cos(2x + 3) and dy / du = 2 u
Use the chain rule f '(x) = (dy / du) (du / dx) = 2 u 2 cos(2x + 3)
Substitute u = sin (2x + 3) above to obtain f '(x) = 4 sin (2x + 3) cos (2x + 3)
Use the trigonometric fromula sin (2x) = 2 sinx cos x to simplify f '(x) f '(x) = 2 sin (4x + 6)

http://www.youtube.com/watch?v=6kScLENCXLg

Calculus/ 2nd six wks/ Assignmnets

10-5-09 Thru 11-11-09

1.Section 3.3/ pg. 125/ #2-42 evens & 46, 47
2.Section 3.6/ pg. 153/ #14-32 evens & 41- 48 all
3.Section 3.7/ pg. 162/ 1-12 all
4.Gateway Quiz Sections: 3.3 & 3.6
5.Section 3.7/ pg. 162/ 13-21 all
6.Related Rates Packet /Any 8
7.Review
8.Test
9.Related Rates Packet /Any other 8
10.Review- xtra credit
11.Six Weeks Test