- In Example 3.7.1, would expanding A(x) have made any of the steps that followed simpler? Would it have made any of the steps harder?
- In Example 3.7.2, would expanding V(x) have made any of the steps easier? Harder?
- Monday is the deadline for receiving full credit on the Differentiation Exam.
- As usual, put plenty of time and effort into studying for Exam 2; spreading your studying time out over several days is harder for some to plan, but much more effective than packing it into one or two days.
- As usual, take advantage of all the Kollett Center has to offer, as well as my office hours.
- Get questions on PS 9 out of the way
**before**class as much as possible, so you can be focusing on reviewing everything for the exam. - Once again, you may have a "cheat sheet", consisting of notes handwritten by you on
*one*side of an 8 1/2 x 11 (or smaller) piece of paper. -
**You may begin taking the exam at 12:30pm Thursday.** - If you have not yet passed the Differentiation Exam, the next deadline is Monday 11/8 at 4pm, for 90% -- study for Exam 2 now, then get back to working on the Differentiation Exam.
- In Example 3.7.5,
- what physically does the quantity 2πr
^{2}represent? How about 2πrh? - The derivative A'(r) is not defined at r=0. Why is 0 not a critical number for A(r)?
- the result the authors arrived at for the values that minimize the amount of material used in a can do not reflect the reality of the design of most 12 oz cans. Did you notice any unrealistic assumptions that were made while working through the problem that may explain this difference?

- what physically does the quantity 2πr
- In Example 3.7.6, why are the only critical numbers those values of x where C '(x)=0?
- For each of the following, answer
*True*or*False*, and give a brief explanation or example for your choice- If there is only one critical point, it must be the minimizer or maximizer that you are seeking.
- If there is only one critical point, it must be a local extremum.
- If there is only one local extremum, it must be an absolute extremum as well.

- Begin working on WW 10 and PS 10 (another group problem set). Once again, switch partners, be primary author if you weren't last time, and don't split up the problems.
- For those who are still working on the Differentiation Exam, the deadline for receiving 90% is Monday 11/8 at 4pm.
- Why might finding the Taylor polynomial of a function be useful?
- In your own words, briefly explain the
*idea*(not just the steps) of building a Taylor polynomial for a function f(x). - The deadline for receiving 90% on the Differentiation Exam is Monday at 4:00pm.
- Write 2
^{-1}+3^{-1}+4^{-1}+5^{-1}+6^{-1}+7^{-1}+8^{-1}+9^{-1}+10^{-1}+11^{-1}+12^{-1}in summation notation. - Write out the terms (
**do not evaluate**) from expanding - What do you think the purpose of summation (sigma) notation is?
- So that I know how much detail to go into ... have you seen sigma (summation) notation before? How well do you feel like you understand it?
- Bring questions on PS 10.
- Remember to put a star next to the primary author's name.
- If you are still working on the Differnetiation Exam, the next deadline is 11/29, to receive 75%.
- Briefly describe how to approximate the area between a curve and the x-axis over an interval [a,b].
- In Equation 4.3.1,

what do f(x _{i}), Δx, and n represent? - Suppose f is a positive decreasing function. Does a
*right sum*(that is, a Riemann Sum using the right endpoints) over- or under-estimate the area between f(x) and the x-axis? How about a*left sum*? - Begin WW 11 and PS 11.
- In Example 4.2, interpret the definite integral (that is, the limit of the Riemann sum) as area.
- Explain why Theorem 4.4.1, which states that if f is continuous over the closed interval [a,b], then f is integrable on [a,b], seems plausible to you.
- Explain why Part ii of Theorem 4.4.2 makes sense graphically.
- Bring remaining questions on PS 11 to class.
- Exam 3 will be on Thursday 12/2, the Thursday after Thanksgiving Break.
- Begin working on WW 12. As usual, because of the exam this assignment will not be graded, but the material on it will be covered on the exam.
- If you are still working on the Differentiation Exam, the deadline to receive 75% on it is the Monday after Thanksgiving Break, Monday 11/29 at 4pm.
- If you are still working on the Differentiation Exam, the deadline to receive 75% on it is the Monday after Thanksgiving Break, Monday 11/29 at 4pm.
- Does every continuous function f have an antiderivative? If so, what is it? If not, why not?
- If you're given instantaneous velocity, how do you find net distance traveled over an interval of time?
- The deadline to receive 75% on the differentiation exam is Monday at 4pm.
- Visit my office hours and visit the Kollett Center while clearing up questions before the exam!
- Get questions on WW 12 out of the way
**before**class. WW12 should be done before class so that you can focus on reviewing. - As usual, you may have a "cheat sheet", consisting of handwritten notes on
*one*side of an 8 1/2 x 11 (or smaller) piece of paper for the exam. - As before, you may begin taking the exam at 12:30pm Tuesday.
- If F and G are both antiderivatives of f(x), how are F(x) and G(x) related to each other algebraically? How are they related to each other graphically?
- What is the difference between an antiderivative and an indefinite integral?
- Begin WW 13.
- If you are still working on the Differentiation Exam, the last day to receive any credit (50%) is the last day of classes (Friday 12/10), at 3pm.
- What do e
^{x2}from Example 4.6.1, (x^{3}+5)^{100}from Example 4.6.2, cos(x^{2}) from Example 4.6.3, (3sin x +4)^{5}from Example 4.6.4, and sin(√x) from Example 4.6.5 all have in common? - Looking again at these same functions and examples -- what did the choice of u have in common in each?
- When calculating antiderivatives or indefinite integrals, how can you always check whether you result is correct (without using a computer or a calculator?)
- I will answer questions on WW 13 on Thursday (or possibly Friday) rather than on Wednesday as is usual.
- The deadline to receive 50% on the Diff Exam is Friday at 3pm.
- If I did not deal with questions on WW 13 on Thursday, then bring them to class Friday.

Fall 2010, Math 101

**November and December, 2010**

**Be sure to check back often, because assignments may change!**

(Last modified:
Sunday, December 5, 2010,
9:17 AM )

All section and page numbers refer to sections from Calculus: Early Transcendental Functions, 3rd Edition, by Smith and Minton. |

I'll use Maple syntax for some of the mathematical notation on this page. (Paying attention to how I type various expressions is a good way to absorb Maple notation). I will not use it when I think it will make the questions too difficult to read.

__ Due Monday 11/1 at 8am__

**Section 3.7: Optimization**

**To read:**
Thru Example 3.7.3. Really read through these examples carefully, paying attention to why the authors are doing each step. In Example 3.7.3, pay particular attention to the transitoin from the distance function d(x) to the function to be optimized, f(x)=[d(x)]^{2} -- this is a useful technique

**Reading questions:**

- In Example 3.7.1 and 3.7.2, the authors caution us not to simplify the function to be maximized out of habit ; although they omit this caution in Example 3.7.3 they again refrain from expanding the function to be maximized.

**Reminder:**

__ Due Wednesday 11/3 at 8am__

**Bring Questions for Exam 2**

**No Reading Questions Today**

**Reminder:**

__ Due Friday 11/5 at 8am__

**Section 3.7: Optimization (continued)**

**To read: **Finish the section. Pay close attention to Remark 3.7.1.

**Reading questions:**

**Reminder:**

** Due Monday 11/8 at 8am**

**Handout on Taylor Polynomials** (available on OnCourse page)

**To read:**
All. I know adjusting to the different style and language can take effort, but be patient

**Reading questions:**

**Submit answers through OnCourse**

**Reminder:**

__ Due Wednesday 11/10 at 8am__

** Handout on Taylor Polynomials (continued)** (available on OnCourse page)

**Section 4.2: Sums and Sigma Notation**

(Note that we are skipping Sections 3.8, 3.9, and 4.1)

**To read: **Re-read the section on Taylor polynomials carefully. Back in your own textbook, you may skip the first 1.5 pages of Section 4.2 -- we're not dealing with the *ideas* of chapter 4 yet, but I thought that the *notation* introduced in this section could help with Taylor polynomials. Begin reading in the middle of page 355, with the sentence that reads "We begin by introducing some notation. " Read through Example 2.3, and also just read the statement of Theorem 2.2.

**Reading questions:**

**Reminder:**

__ Due Friday 11/12 at 8am__

**Introduction to Chapter 4**

**Section 4.3: Area**

**To read:** Skim through all. Don't get too hung up on the notation and the vocabulary -- at this point, I'm mainly concerned with the big ideas of undertanding using rectangles to approximate area.

**Reading questions:**

__ Due Monday 11/15 at 8am__

**Section 4.4: The Definite Integral**

**To read:** All

**Reading questions:**

**Submit answers through OnCourse**

__ Due Wednesday 11/17 at 8am__

**Section 4.4: The Definite Integral**

**To read:** All

**Reading questions:**

**Reminder:**

__ Due Friday 11/19 at 8am__

**Section 4.4: The Definite Integral (continued)**

**To read:** None

**No Reading Questions Today!**

**Submit answers through OnCourse**

**Reminder:**

__ Due Monday 11/22 at 8am__

**Section 4.5: The Fundamental Theorem of Calculus**

**To read:**
None yet - because I plan on approaching the section in a slightly different order than the text does, I think you'll get the most out of the reading if you wait and read the whole section for next Monday.

**No Reading Questions: Today**

**Reminder:**

__ Due Wednesday 11/24 at 8am__

**Thanksgiving Break**

**No Reading Questions Today, Of Course**

__ Due Friday 11/26 at 8am__

**Thanksgiving Break**

**No Reading Questions Today**

__ Due Monday 11/29 at 8am__

**Section 4.5: The Fundamental Theorem of Calculus**

**To read:**
All.

**Reading questions:**

**Submit answers through OnCourse**

**Reminders:**

__ Due Wednesday 12/1 at 8am__

**Bring Questions for Exam 3**

**No Reading Questions Today**

**Reminders:**

__ Due Friday 12/3 at 8am__

**Section 4.1: Antiderivatives**

**To read:**
All. Pay particular attention to the concept of the indefinite integral; the rest of the section should be review so you can probably just skim the rest.

**Reading questions:**

**Submit answers through OnCourse**

**Reminders:**

** Due Monday 12/6 at 8am**

**Section 4.6: Integration by Substitution**

**To read:**
All except for Example 4.6.8

**Reading questions:**

**Submit answers through OnCourse**

** Due Wednesday 12/8 at 8am**

**Section 4.6: Substitution**

**To read:**
Review

**No Reading Questions Today**

**Reminders:**

** Due Friday 12/10 at 8am**

**The Big Picture**

**No Reading Questions Today**

**Reminders:**

**Janice Sklensky**

**Wheaton College**

Department of Mathematics and Computer Science

Science Center, Room 101A

Norton, Massachusetts 02766-0930

TEL (508) 286-3973

FAX (508) 285-8278

jsklensk@wheatonma.edu

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