Nifty Integrator Tool

http://integrals.wolfram.com/index.jsp

-Mr. Morgenbesser

Slope Field Web Pages

Check out these web pages and explore the slope fields on the handouts from class today:

The first one: http://alamos.math.arizona.edu/~rychlik/JOde/JOdeApplet.html

And the second one:http://jlearn.mit.edu/simulations/mappingfields.jnlp

Enjoy!

-Mr. Morgenbesser

HW for Unit 3: Applications of Derivatives

HW #37: Assigned on 11/30/2006: Related Rates p. 324: 1-8 all, 11-17 odds only

HW #35: Assigned on 11/28/2006: Newton's Method p. 293: 11-15

HW #34: p. 294: 48, 53, 55, 58

HW #33: p. 293: 39, 40, 41

HW #30: Linearizations: Assigned on 11/15/2006:
Beginning on p. 241 Read and go through "Explorations" #2 and #3.

HW #28: Assigned on 11/13/2006:
p. 270: 1-9 odds and 15-19 make the line graph with the plusses and minuses like we did in class

Lesson #27: (In class on 11/10/2006): Read and Copy Notes that are distributed by substitute teacher on Absolute (aka Global) and Local (aka Relative) Maxima and Minima. (aka Extrema). Do copy all of the notes and examples into your own notebook with your own hand! Do process it carefully and make sure that you understand the terminology and the examples. In class do problems on p. 194 of the handout odd numbered problems from 11-31.
HW #27: Assigned on 11/10/2006:
On p. 194-195 of the handout do even numbered problems from 6-18, and do number 53.

Public Service Announcement Assignment

We, the members of the Citizens Promoting Awareness of Calculus, have been given the opportunity to place full-page advertisements in various popular magazines.

Create a full-page advertisement that will promote awareness of the properties that are demonstrated in the summary table that we put on the board during Lesson #30. (Based on the summary table on page 282 of your text book). You can also choose something else that we have covered if it is connected to these ideas.

You may parody popular advertisements and the popular media or come up with something completely unique. You can assume some knowledge of calculus- you are promoting awareness but you don't have to make it an "instructional" poster. Although, you may include instructions in your advertisement as well. You may hand-draw, cut-and-paste (with real scissors and glue), use a computer, or a combination of all three.

In other words, you've got a lot of freedom to be creative. If you find the open-ended nature of this assignment intimidating, then feel free to just make a really clear one-page illustration of an important idea that we've covered.

We'll share the finished posters in class on Wednesday November 22nd. I look forward to seeing them!

First Term POW- Due November 3rd!

Download Printable Version
Problem Statement:

A particle moves along the y-axis so that its position at time t>=0 is given by the function s(t)=2t³-21t²+60t+6.

1. Find the velocity and acceleration functions of the particle

2. Describe the motion of the particle from 0<=t<=7. Give algebraic justification for your answer.

3. Draw the position, velocity and acceleration functions on the same axis and make connections between the three graphs.

4. Find the velocity and acceleration of the particle at time t=2 seconds and make connections to the graphs.

5. Find where the speed of the particle is increasing and where the speed of the particle is decreasing. Justify your answer.

6. Find when the particle reaches its highest point. Justify your answer.

Please write a report that thoughtfully and completely answers each of the questions above. The format of the report should be as follows:

Introduction or Overview: Your introductory paragraph must include what the purpose of this paper is – what is the major objective of the problem? What question(s) are you trying to answer? What background information is necessary for the reader?

Process, Observations and Results: Answer each of the questions above and tell the reader what process you followed and what you observed using diagrams, graphs and calculations to support your explanations. Describe any relationships, similarities, differences, equivalences or anything interesting and relevant that you found as you went through the process.

Discussion and Reflection: Give your personal reaction to the project. Make connections between this project and other things in your mathematics repertoire, your life, and the world.

Olympiad Location 10/24

You should just come up to the "math hall" on the fourth floor of downs building- we will be placing students in rooms in that hall alphabetically.

Go to homeroom and then come directly upstairs instead of going to your first period class!

See you soon,
Mr. Morgenbesser

Homeworks for Unit 2: Derivatives

HW #25: Assigned on 11/2/06:
Inverse Trigonometric Derivatives and Exponential Derivatives: p. 594: 1-17 odds, p. 556: 1-13 odds. And REMEMBER the POWS are DUE TOMORROW!

HW #22: Assigned on 10/26/06:
Implicit Differentiation: p. 238: 29-32.

HW #21: Assigned on 10/25/06:
More Chain Rule: p. 227: 15-51 (only the multiples of 3).

HW #20: Assigned on 10/23/06:
Chain Rule: p. 227: 1-13 odds only.

HW #19: Assigned on 10/20/06:
Trigonometric Derivatives: p. 219: 5-23 odds only.

HW #18: Assigned on 10/16/06:
Position, Velocity, and Acceleration: p. 211: problems 8-10.

HW #17: Assigned on 10/13/06:
Parametric Mode and Moving Particles: p. 210-211: problems 1-6. (These aren't quick problems; give yourself some time and look at each graph and the derivatives and think about the movement of the particle).

HW #16: Assigned on 10/12/06:
Differentiation Rules (continued)! p. 196: 25-28, 41-45 odds, 67, 78. And "the rock problem":
A Dynamite blast blows rock up w/ a launch velocity of 160 ft/sec (~109 mph). It reaches a height s(t)=160t - 16t². Use your calculator to answer a-d: (a) Graph the rock's height as a function of time. (b) How high does the rock go? (c) How long is it in the air? (d) How fast is the rock going when it is 256 feet above the ground? (e) Confirm your answers analytically.

HW #15: Assigned on 10/11/06:
Differentiation Rules (continued)! p. 196: 2-16 evens, 17-23 odds.

HW #14: Assigned on 10/6/06:
Differentiation Rules! p. 183: 25, 39, 40. p.178: 31, 33. p. 196: 1-15 odds.

HW #13: Assigned on 10/5/06:
Lucky you! No homework tonight, but be super ready for your Friday quiz!

HW #12: Assigned on 10/4/06:
More with the Limit Definition of Derivative and Using the nDeriv Function: p. 178 #14,16,18,19,20. (I think that's what I said anyway). For each of these verify your derivative using you calculator and nDeriv at x=3.

HW #11: Assigned on 10/3/06:
Introduction to Derivatives: p. 178 #7,9,13,15,17

Files for Tuesday and Wednesday

Here are Position, Velocity, RemoteControl, and Motion.

Enjoy!

-Mr. Morgenbesser