Monthly Schedule

(Honors AP Calculus, Period C)

M 10/1/07

HW due: Read §§3-8 and 3-9; write §3-8 #1.

 

T 10/2/07

HW due: “Chain Rule Challenge.” With your study buddy, develop a function that is difficult (but not impossible) to differentiate. Throw in some heavily nested functions and an occasional disguised constant if you wish. See if you can stump your friend. Save all your written work so that your answers and notation can be double-checked in class.

 

W 10/3/07

HW due: Write §3-8 #2, §3-9 #1-23 all, 25. If you take more than 15 seconds per problem for the first few in §3-9, you need to practice more. Some of them are done for you below as examples. Remember, the setup (statement of the problem) is required in each case. Use correct notation; simplification is optional.

1.

2.

3.

4.

5.

11.













 

Th 10/4/07

HW due: Read §4-2; write p. 127 #T17, §4-2 #3-23 eoo, 35.

 

F 10/5/07

Faculty professional day (no school).

 

M 10/8/07

Holiday (no school).

 

T 10/9/07

Test (100 points), entire year through §4-2. The review problems and sample tests at the end of each chapter furnish ample opportunities for preparing for the test. Class notes (e.g., taxonomy of differential equations, chaos) may also be covered. For example, even though the book has not yet covered the antiderivative of

y = f (x) = x–1,

nor the derivative of exponential functions such as

y = f (x) = 4x,

you are expected to know them. There will be at least one difficult chain rule question, and you need to be sure that you know both the IVT (§2-6) and the EVT (#13 on p. 70, which was assigned).

A rigorous solution to §2-6 #14, which was also assigned, is now available. This is too long a proof to be included on a test in anything other than a fill-in-the-blank format, but you should be able to read it and learn from it.

 

W 10/10/07

HW due: Read §§4-3 and 4-4; write §4-3 #9, 11, 15, §4-4 #23. Do #23 two ways: (1) using initial simplification, and (2) using QR, without initial simplification. Verify that both methods produce the same result.

 

Th 10/11/07

HW due: Since this posting was late, you are required to do only the one problem that was given during class, namely §4-5 #29. If time permits, please also read §4-6.

 

F 10/12/07

Notice: Class will meet today in Steuart 302.

HW due: Read §§4-6 and 4-7; write §4-5 #9, 12, 23, 26, §4-6 #32.

 

M 10/15/07

HW due: Read §4-8; write §4-7 #1-7 odd, 8, 10.

 

T 10/16/07

HW due: Read §5-3; write §4-8 #3-15 odd, 19, 21, 26.

 

W 10/17/07

HW due: §4-9 #R1, R2c, R3c-e, R4a, R5a, R6, R7, R8.

 

Th 10/18/07

Notice: Class will meet today in Steuart 302. If possible, seniors should submit HW for both today and tomorrow, since tomorrow’s absence is preplanned.

HW due: §5-2 #2-15 all, 17a, 17c.

 

F 10/19/07

HW due: Finish all Chapter 4 review problems that were due 10/17; write §5-12 #R2, R3, R4.

Note: Today is the Form VI retreat. HW from seniors will accepted without penalty until 3:15 p.m., although I would prefer it one day in advance since the retreat is a preplanned absence.

 

M 10/22/07

HW due: Read §5-4; write §5-4 #3-42 mo3, 46.

 

T 10/23/07

Test (100 pts.) on all of Chapter 4, plus §§5-2 and 5-3.

Notice: Today’s test will be administered in Steuart 302, not the usual Mathplex classroom.

 

W 10/24/07

HW due: Read §5-5; write §5-5 #7, 8, 9, 12.

 

Th 10/25/07

Optional Test (100 pts.) on Chapter 4, plus §§5-2 through 5-5. This test is for students who wish to drop a low test score. Per our earlier agreement regarding 4 tests, I am willing to drop the lowest score for any student who has 4 test scores, but there was no time during the quarter to squeeze in a fourth test covering a new block of material. Please note, since this test is optional, no make-up test will be offered. If you miss it for any reason, your average will simply be based on your other 3 tests, HW, and quizzes.

If you “bomb” this test (i.e., earn a score lower than any of your other tests), there is no penalty.

If you are happy with the average of your other 3 tests, please come to class for roll call, and then you may use the remaining time as you see fit. If you wish to use the time for sleeping or uninterrupted study for another class, without having to tromp all the way up to the Mathplex, then I would ask that you make arrangements with me beforehand so that I know not to report you as AWOL for the class period.

 

F 10/26/07

Last day of first quarter.

HW due: Read §5-6; write §5-6 #3, 4, 5, 6, 11, 42. Note: #42 is printed below.

42. Copy the following compact statement of MVT onto your HW paper several times:

       f cont. on [a, b], f diff. on (a, b)

Note: For most students, 3 or 4 times is probably enough. If your memory needs more practice, you may wish to repeat the drill several more times. The MVT is the second or third most important theorem in the entire course. You must know the exact statement of the hypotheses and the exact statement of the conclusion, including the fact that c is guaranteed to exist within the open interval from a to b.

 

M 10/29/07

HW due: Finish any of Friday’s problems that still need to be worked on. Then, read §5-7 and work the problems below. There are a lot of problems, but each one is quite short and should take you no more than a few minutes.

1. Compute, with your calculator, the value of .

Show that a Riemann sum involving only one interval achieves acceptable results if the sample point is chosen at the midpoint (i.e., x = 3.75) but achieves excellent accuracy if the sample point is chosen to be 3.80277564. Use the full accuracy of your calculator (8 or more decimal places) to compute all of these results.

2. Consider the function g(x) = x3/3 – 2x2 + 13x. Compute the secant slope (i.e., average rate of change) for function g(x) on [3, 4.5].

3. Does g(x) satisfy the hypotheses of MVT? Verify each one and list them.

4. Find the value c that satisfies MVT on [3, 4.5], i.e., c such that . Show work.

5. Let f (x) denote the integrand in #1. What is the relationship between f and g?

6. Compute, with your calculator, the value of .

Show that a Riemann sum involving only one interval achieves poor (unacceptable) accuracy if the sample point is chosen at the midpoint (i.e., x = –0.115) but achieves excellent accuracy if the sample point is chosen to be 0.7596231396. Use the full accuracy of your calculator to compute all of these results.

7. Consider the function v(x) = e2x/2. Compute the secant slope (i.e., average rate of change) for function v(x) on [–2, 1.77].

8. Does v(x) satisfy the hypotheses of MVT? Verify each one and list them.

9. Find the value c that satisfies MVT on [–2, 1.77]. Show work. (Solve an exponential equation.)

10. What coincidence do you notice between #9 and #6? between #4 and #1?

11. Let u(x) denote the integrand in #6. What is the relationship between u and v?

12. Repeat steps 1-5 using a different integrand of your choice and a randomly chosen closed interval.

13. Answer #13 on p. 215. Write your conjecture carefully, avoiding any use of the word “it.” If you did #12 carefully, then you have already verified that your conjecture seems to work!

 

T 10/30/07

HW due: Read §5-8, which is the absolute core of the course. No additional written work is due; please take another shot at yesterday’s assignment if necessary. It will be evaluated a second time.

 

W 10/31/07

HW due: Read §5-9; write §5-8 #Q1-Q10, #1, 3, 7, 9.

 

 

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Last updated: 10 Nov 2007