**Problem of the Week**

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people:mckenzie:math_220_hw

Homework for the night of (due the following class day):

**Thurs Jan 19** Read Sec 1 and Sec 2; do problems Sec 1, p 5, 1, 2, 7, 8; Sec 2, pp 15-16, 1-13

**Fri Jan 20** Read Sec 3 and Sec 4; do problems Sec 3, pp 26-27

View Break even problem 1, Break even problem 2 : Use derivative to find eqn of tangent line Ex 1 and Ex 2

**Mon Jan 23** Quiz on Sec 1, 2, 3 will be Wednesday.

Read Sec 4 again. Some helpful videos.

Solving exponential equations without and with logs

3 examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

Do p 43 #1-5, 8 b e f g, 10 a c e f, 11 e f h, 12, 14 b, 17 a, 20 d e, 21 b d f

**Wed Jan 25** Read Sec 5 and view *comprehensive* video lecture on compound interest problems:

The value of a loan or investment over time can be given by *P*(*t*) or *A*(*t*). Both stress functionality with respect to time.

Do Sec 5 p 56 #1-7

An interesting video is Understanding the number e (exponential growth).

**Thurs Jan 26** Do Sec 5 p 56 #1-7.

Refer to Interest formula summary.

Another good interest video is found at Tarrou's interest lecture

Read Sec 6 Limits and go to videos to view the video on limits. Do neat work and box your final answer. You don't have to print the pdf; loose leaf is fine.

**Fri-Sun Jan 27-29** After looking over Friday's notes and rereading Sec 6, do Problems Sec 6 p 66 #1-12 all and #16-30 even. These videos are helpful.

Evaluate limits using properties, Ex 1 and Ex 2

More techniques for evaluating limits, Ex 1, Ex 2, Ex 3

Infinite limits in which a function goes to positive infinity or negative infinity as x approaches a.

**Mon-Tues Jan 30-31** Test 1 will be on Wed Feb 8. It will cover Sections 1-9 of the book.

Read Sec 7 and Sec 8. Go to Videos and *view all* for this section. Many examples fully worked.

Do Sec 7 p 72 #1, 2, 3

**Wed Feb 1** Reread Sec 8; do p 78 #1, 2, 3, 4

The skill is to find the equation of the line tangent to some curve f(x) at a given value of x, using the derivative and point-slope form of a line.

**DUE THURS**: Take-home quiz, as handed out today. The guidelines for take-home assignments (unless otherwise stated) are these:

- You may use your notes and text, and even the videos.
- Work independently (no study partner or tutor may help you).
- Work neatly and staple or use paper clip on multiple pages.

No late quizzes will be accepted, so be sure you are present to hand it in. I aim to give it back on Friday so you have it to study.

Though you may use notes, the length of this quiz is about half the length of the exam, so aim for a half hour. If that isn't happening, you know what you need to prepare more over the weekend.

**Thurs Feb 2** Read Sec 9. View all three Videos on continuity.
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Do Sec 9 pp 84-85 #1 a-e, 2 a-d, 4, 5, 6

**Fri-Sun Feb 3-5** These three statements must be satisfied if a function for f(x) to be continuous at a in the domain of f:

f(a) exists

lim f(x) = L as x approaches a

f(a) = L

Prepare questions on Sections 1-9 for a review class on Monday. Review the videos where you had problems or weak understanding. A concise list of skills/topics will be posted here for your reference.

Exam 1 is Wednesday.

**Mon-Tues Feb 6-7** Study for Exam 1 Secs. 1-9 topics

Do page 1 only of this Cost/revenue/profit pdf

Here are some extra videos on finding this type of function: Cost/revenue/profit 1, Cost/revenue/profit 2 and Cost/revenue/profit 3

**Wed Feb 8** Read Sec 10

**Thurs Feb 9** Do p 92 #1-6, #8-10

Read the supplemental: Overview of derivatives as marginal functions, with illustrative example

**Fri-Sun Feb 10-12** Read Sec 11; do pp 97-98 #1, 2 b c f g l m, 3 a-d, f l m, n, #4 a, #6

Check out the Derivative videos and synopsis

Do Sec 10, p 93 #15, 16; Sec 11, pp 98-99 #7, 13 c e f g h j m

**Mon-Tues Feb 13-14** Read Sec 12; watch the video again (read my synopsis on the Video page). Also, view

You might not understand this topic fully. It's a flip learning night.

Go back to Sec 10 and do on pp 92-93 #11, 12, 13

**Wed Feb 15** Do problems in Sec 12 p 107 #2, 4, 5

Read Sec 13.

**Thurs Feb 16** Study for Friday quiz on Secs. 10, 11, 12.

Do Sec 13 #1, 2, 3, 4, 8

Read Sec 14 (related rates) and view the related rate videos (read my synopsis on the Video page).

￼Related rates 1: Area of circle and changing radius rate

Related rates 2: Area of triangle and changing side length rate

**Fri Feb 17** Related rates 3: Ladder sliding down the wall problem

**Mon Feb 20** Read Sec 14 again and videos again. Add Cost and profit with respect to time

Do pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14

**Wed Feb 22** Read Sec 15.

**Thurs Feb 23** View:

Finding critical numbers of a fcn

Do pp 129-130 #2, 4 a-i

To hand in–instead of the one handout out today

Here's a previous semester's derivative quiz. *Do it as practice without using notes.* Check against my answers tomorrow.

**Friday Feb 24** Read Sec 16 and view short videos on these theorems (not included on test but need to start them to be on schedule, since we have an extra day before the test than two other sections).

Do p 136 #1, 2

Also, try this Implicit and critical number practice quiz.

Since we don't have the first derivative test (FDT) yet, you determine if x = c is an extreme is a local max or min from checking values very close to either side of each c. We'll be glad to have the FDT after the exam to do this!

**Exam 2 preparation topics**

Basic derivative forms (power, log and exponential)

Operations on derivatives (not discussed much but we have done automatically, like f'(cx) = cf'(x), (f + g)'(x) = f'(x) + g'(x), and so on.

Derivative of a product, quotient, and the use of the chain (composition) rule (all these entail the derivative forms in combinations)

Higher order derivatives, with Leibniz and other notation

Evaluating a function and its derivative at a given x

Finding equation of a tangent line using implicit differentiation

Marginal cost, revenue and profit phenomena again (non-linear functions this time)

Related rates (know very basic geometric formulas)

Critical points of a function (what they are and how to find them), local extrema (max and min)

On Monday you will have a handout with extra practice problems. I WILL NOT POST THIS. If you want it you have to come to class. If you have a valid absence, notify me.

**Tues Feb 28** Keys to related rates and Exam 2 review

Note: I have added a problem at the end of the key, the multipart problems #13 on operations on derivatives.

**Thurs-Tues Mar 2-7** With the very long weekend ahead, please view several videos covering the next few sections, critical numbers and local max, min; first and second derivative tests on the Video page

Read Sec 17 and 18, and my notes:

**Wed Mar 8** Do Sec 17, p 141 #1, #2a-m

**Thurs Mar 9** Read over my Notes on First and Second Derivative Tests

Continue watching the videos for FDT and SDT.

Read Sec 18; get to work on Sec 18 pp 148-149 (Do #3 before #2) #1, 3 a-e, 2 a, b, e, f, h

Study for a quiz tomorrow (Friday) on what we did today (Steps 0 to 7 for analyzing intervals of increase, decrease, and local extremes.)

**Fri-Sun Mar 10-12** Okay, now you can do that Sec 18 hw, plus the examples on the overhead today. Show by calculus that the increasing, decreasing, concavity and crit values are such that we see in the graphs.

**Mon-Tues Mar 13-14** View the next section of videos, those covering curve sketching, on the Video page

**Wed Mar 15** Snowstorm Stella homework:

Read Secs 19-21.

View Sketching rational functions and Sketching another rational function

Read Sketching rational function notes

**Thurs March 16** Read some of my older notes on Curve-sketching book examples

and More curve-sketching book examples (These contain some Sec 18 HW problems, so see the solutions link, too)

View Sketching a polynomial with FDT and SDT and Sketching a more involved rational function with FDT and SDT

To hand in Friday, March 17, St Patrick's Day. (Missed celebrating Ides of March on the 15th due to the snow.)

Take-home quiz on polynomial sketching

**Fri-Sun Mar 17-19** Sec 19-22 HW cover the skills we have now discussed fully.

For example: Limits at infinity, which relate to horizontal asymptotes (including "tricks" at 6:16) and Detailed examples of first and second derivative for graphing a function

Do Sec 19 #1 a, b, c, #2 a, b

Do Sec 20 pp 167-168 #1 a, b, c, #3, #4 a-g, #5 c, d, e, f

Read How to find absolute extrema of a function on a closed interval

OK to skip Sec 21 problems.

Do Sec 22 p 185 #3 a, b, d, e

**Mon-Tues Mar 20-22** Read Sec 23

View:

Optimization problem (instructive)

Do p 192 #2-5, 6, 9, 10, 12, 15, 16

**Wed-Thurs March 23-24** Read Sec 26 (Functions of Two Variables) and Sec 27 (Partial Derivatives)

View Partial derivatives

Don't worry if you don't fully understand the three-dimensional nature of the discussion. Our 'dimensions' are not geometric, but this is the avenue that the derivative is explained.

Do Sec 26 p 212 #1-4, #6-8

Do Sec 27 p 212 #1 a-c, e, f, i

**Fri Mar 24** *Note*: We'll put off Sec 28 Extrema in 3-dim until Monday.

To the Sec 27 assignment already posted for today I've added Sec 29.

View Second order partial derivatives

Read Sec 29. View Optimization via Lagrange multiplier

Do problems p 233 #2 a b c e, 4, 6, 7

*Mini-quiz Monday*: On partial differentiation, find the first and second partials, pure and mixed, of a couple of multi-variable functions.

**Mon-Tues Mar 27-28 ** Read Sec 28 and see my Notes and Detailed Example Sec 28 in which I explain why the criteria of the SDT using D(x,y) makes sense.

View:

More examples local max, min and saddle point by analyzing D value

Local extremes and saddle points of multivariate function

Do p 226 #1 a-e,i #2

**Wed Mar 29** View Elasticity of Demand

Read Sec 24, Elasticity

Do p 199 #1-5. Read over my summary here, but don't print. I'm editing it and will have copies tomorrow.

Final revised summary of elasticity (my notes)

**Thurs Mar 30** Do p 199 #6-9

Prepare questions on any of the topics in the covered chapters to begin review on Friday.

Short quiz on elasticity and setting up a Lagrange problem.

**Friday Mar 31** Study for Exam 3. Continue preparing detailed questions for rest of review on Monday.

I revised my Summmary of elasticity

Per your request, I will find some review questions from my own previous quizzes/tests. Watch this space. Or wait till Monday while you go over the HW to date.

The test covers Sec 17-24, 27-29.

**Mon-Tues Apr 3-4** Over the next day I will post older materials, including several that were from my actual quizzes. With answers, since there is no time to do in class.

1. Here is an old quiz I gave on the D test, all worked out. Write the question and try it on your own, comparing your answers to the one on the quiz key.

Quiz and solution on extremes in 3-space

2. We didn't review global (absolute) extremes on closed intervals. An easy topic but worth reviewing:

Finding absolute extremes on closed interval

3. Sketching a polynomial and a rational function

An important note: The SDT is not used to discover whether a critical point is a max or min, but to confirm that a value where f''(x) = 0 is a POI. But to check that I had concluded the max or min properly from the FDT, I plugged my crit pts into the second derivative and checked the sign. Negative means the critical point lies in *an interval* of concave down, hence I should have concluded that critical pt gave a local max. And vice versa.

4. Partial differentiation practice

5. Elasticity problems and Elasticity solutions

Final Unit: Integration

**Thurs Apr 6** Read Sec 30 and view the first video under the Integration unit videos.

**Fri Apr 7 to Tues Apr 18** View Finding a particular F(x), given initial conditions (xo, yo)

**Wed April 19** *Integration catch-up:* Know rules of antidifferentiation, pp 237-238 (basically the same as video and handout/pdf above)

Complete problems in Summary of antiderivative rules, practice problems

Helpful videos to watch again: Indefinite integrals (basic examples) Finding a particular F(x), given initial conditions (xo, yo)

NEW: Read Sec 31. View u-substitution and Another u-substitution Do p 242 #1 a-i

**Thurs April 20** Do p 248 #1 a b c e f g i j k l

Study for Friday quiz on Sec 30 and 31

Read Sec 32 Integration by parts. View Integration by parts made easy

**Fri-Sun April 21-23** Do problems p 255 #1 a b c d e g h i k (see video and examples in text)

Read Sec 33, Finding a Definite Integral

**Mon-Tues April 24-25** This week we cover the Fundamental Theorem of Calculus.

There are two parts to this theorem. We generally use the second part, which is what we need to find the value of a definite integral. To that end, watch Fundamental theorem of calculus part II

(The theoretically deeper but fascinating Fundamental Theorem of Calculus Part I is at the video link)

View Patrick's definite integral examples:

Example 1 of finding a definite integral

Example 2 of finding a definite integral

Do p 260 #1 a-e i j k o p q

Finally, for Wednesday, read Sec 34, Definite Integral and Area.

Then view this important video: Finding area between two curves

**Wed April 26** Do p 268 #1 a b e f, 4, 6 a c g, #5, #8, #9

**Thurs April 27** Add to p 268, problem #6 (we did a few in class).

Read Sec 35. This is a DENSE section that covers far more than the title suggests.

The road map:

- Riemann sum (area of rectangles of ever-increasing number approaches the area under the curve, i.e., the definite integral;

- average value of a function, which is neat because it tells us what value the function attains on an interval via the definite integral divided by the width of the interval;

- total value of a function, which is basically the FTC applied to a marginal or other rate function, whose antiderivative is the sought after function, say cost fcn, value fcn, any quantity given a rate of change of that quantity;

- present and future value of an investment through a constant flow of money (“income stream”) at continuous compounding (this is the analogous case to the Sec 5 topic of present and future value of a one-time investment).

The rest of the unit focuses on this last topic. I will have some handouts to help with this road map.

Quiz tomorrow! Sec 30-35 (up through average value)

**Fri-Sun April 28-30** Do the last quiz again for practice. I added a problem at the end.

View Average value of a function

The average value of a function is actually the mean value theorem of integration.

Read the rest of Sec 35, on Present and Accumulate (Future) Value of an Investment.

The difference from the Sec 5 topic, as I've said, is now we consider a continuous flow of money (an income stream, like an investment or a business venture).

Do p 278, all. The ones I have solutions prepared for are #1 a, d, 2, 4 a, 6-9, 11, 12, 15.

**Mon-Tues May 1-2** I'll post notes with guidelines on 'When to use u-sub and when to use udv'

I'll also post the new summary of the unit's formulas later, or tomorrow.

**Wed-Thurs May 3-4 ** Study for Exam 4. See email for focus problems.

**Fri-Mon May 5-8** Review for final exam.

There will be a review class in WH 329 on Wednesday May 10 from 10 a.m.–noon

people/mckenzie/math_220_hw.txt · Last modified: 2017/05/09 23:55 by mckenzie

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