Homework+!


 * Homework for AP Calculus 2014-2015

__ **no major projects :-)** __.
 * Directions to sign up for www.getafive.com - (They also have AP courses in AP US, AP World, and AP Biology.

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 * 1) 1. Visit getafive.com and click on "I'm a student".
 * 2) 2. On the students page, choose "AP Calculus AB".
 * 3) 3. On the AP Calculus AB page, click on the "Enroll now" button.
 * 4) 4. Create an account or log in if you're already signed up.
 * 5) 5. You're now in your personal Study Room.
 * 6) 6. Click on the "Join a Class" tab on the left and enter this code: Y4F7AM6 (this is my AP Calculus)

1) here are links to the first three tutorials at http://www.calculus-help.com/tutorials/
 * Due: Monday, 9/15/2014 **

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3) Read section 2.4 in Anton (white textbook). ... 2.4 Limits (Discussed More Rigorously) Isaac Newton came up with the basic ideas of calculus during a hiatus from college during the Great (bubonic) Plague (1666-1667). Gottfried Leibniz discovered those major ideas working largely independently a few years later. Calculus revolutionized the western world! During the 18th century scientists and mathematicians were applying the calculus to all sorts of things in an amazing era of discovery. What was even more phenomenal, perhaps, is that the 18th century discoveries were made without a proper 'definition' of a limit. (In mathematics the usual situation is that nothing ever gets done until everyone agrees on a definition). In the latter part of the 19th century, a lot of work went in to creating this proper definition, and this is the main (and only) point for 2.4

Definition!! Begin memorizing the sentence beginning with "We will write". --

1) Read section 2.3 in Anton (white textbook) ... 2.3 Computing Limits: End Behavior The book talks about the limit ideas behind what you learned as 'end behavior'. You have accumulated some ideas of how to determine the end behavior for **polynomials** and **rational functions** (ratios of two polynomials). As I have mentioned, we will be studying functions **IN GENERAL** during calculus, and not limit ourselves to a half-dozen families. And since the idea of end behavior is important, we re-"define" the idea of end behavior as a limit to positive or negative infinity. Nicely, this new definition gives us answers that agree to the 'intuitive' end behavior ideas you learned in Precalculus or Integrated Math 4.
 * Due: week of September 8-12 sometime**

Some basic limits to infinity Limits of x^n (degree of polynomial important - at least whether it's odd or even) Limits of polynomials (high degree term dominates) Limits of rational functions (and an important technique to remember) Limits of functions involving radicals (including two other techniques) First introduction to indeterminate forms of type infinity - infinity

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 * Due: Monday, 9/8/14**
 * 1)**

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1) here are links to the first three tutorials at http://www.calculus-help.com/tutorials/
 * Due: Tuesday, 9/2/2014 **

[] http://www.calculus-help.com/when-does-a-limit-exist/ http://www.calculus-help.com/how-do-you-evaluate-limits/

2) Read the article 'Fun with 0.999...=1. You can find at: http://www.rowan.edu/colleges/csm/departments/math/facultystaff/osler/my_papersl.htm (it's #32)

3) Read section 2.1 and 2.2 in Anton (white textbook). ... 2.1 Limits (An Intuitive Approach) Important terms / phrases / ideas: . Ideas I absolutely hate about this section. If you are not careful, you will get the idea that you find a limit by plugging values into a calculator. NO NO NO!!! They do this here because you are 'getting used to' the idea of what a limit is. You will NEVER get points on any exam if you try to find a limit by plugging in a bunch of numbers closeby. . ... 2.2 Computing Limits Now we move away from the idea of limits to actually being able to figure some limits out. Important terms / phrases / ideas: Basic limits Theorems about limits and limits of combining functions in different ways Limits of polynomials and rational functions Limits that do not exist Indeterminate forms of type 0/0 Limits involving radicals Limits of piece-wise defined functions -- []
 * syntax of limit statement
 * one sided limit; two sided limit
 * left hand limit; right hand limit
 * limit of infinity (vertical asymptote)
 * limit at infinity (horizontal asymptote)
 * Early reading**