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people:mckenzie:math_220_hw

Scan of Chapters 1, 2, 3 of text

Homework for Week 1

In bold is the date on which the assignment is given. Do them so you may ask/answer questions the following class day.

**Wed Aug 23** Read Sec 1 and Sec 2; problems Ch 1, p 5, #1, 2, 7, 8; problems Ch 2, pp 15-16, #1-13

**Thurs-Fri Aug 24-25** Catch up on Ch 1 and 2 problems and study for quiz on this material (especially from your notes).

Read Sec 3.

HOMEWORK FOR WEEK 2

**Mon Aug 28** View first two videos under Cost, Revenue, Profit at Videos

Do problems Sec 3, pp 26-27; do take-home Quiz 1

**Wed Aug 30** Check out the full solutions to Sec 3 at HOMEWORK SOLUTIONS

Read Sec 4 and study the handout Properties of exponents and logs.

View these helpful videos to preview what we cover tomorrow.

Examples of solving an exponential equation

Example of solving a logarithmic equation

Another example solving a logarithmic equation

**Thurs Aug 31** Do Sec 4 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

Mini-quiz tomorrow on linear cost, revenue, profit functions (including concept of marginal cost). *You* will find the functions given data. See your homework for typical question, like “find x to break even”.

**Friday Sept 1** Read Sec 5 and view *comprehensive* video lecture on compound interest problems.

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

Finally, an interesting video Understanding e (exponential growth).

A point about the variables used: The value of the principal (whether loan or investment) *P* as time passes is often given as *F*, and sometimes *A*, as in the video. These are *y* values, the dependent variable.

I often stress the *functional* nature of these. They represent growth (money, population) over time. That is why I will often write *P*(*t*) for *F*. In the first video the teacher uses *A* for final account value. I would like to see *A*(*t*) (for account value over time).

After doing the reading and watching the video, try Sec 5 p 56 #1-7. They are not difficult. Here are some clear formula notes and the algorithm (applied as learned in the previous chapter) to solve an interest problem:

Although we will do Sec 5 on Wednesday, since it's a long weekend and we don't meet again till Wednesday, please get a jump on the enjoyable calculus topic of limits by viewing the first “Limits” video at Video link.

HOMEWORK FOR WEEK 3

**Mon Sept 6** Now you can do the Sec 5 problems.

Also, I will cut down the number of Sec 4 log and exp problems, and focus on only essential skills.

**Wed Sept 6** Read Sec 6; view the videos on limits:

**Thurs Sept 7** Do Sec 6, p 67 #1-12

Study for Friday's mini-quiz on compound interest and a few log and exp short answers.

HOMEWORK FOR WEEK 4

**Fri Sept 9** After looking over Friday's notes and rereading Sec 6, try again Problems Sec 6 p 66 #1-12 all, if you haven't done them already, and #16-30 even. Study the posted solutions.

More good videos:

Evaluate limits using properties, Ex 1 and Ex 2

More techniques for evaluating limits, Ex 1 (which gets a little jump on the idea of continuity; for our purposes this is simply the feature of a function which can be drawn by not lifting your pen).

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

**Fri-Sun Sept 9-11** See summary of limits, including some important ones not explicitly stated in sec 6 (which I'll post tomorrow)

Read sec 7.

**Mon Sept 12-Tues Sept 13** Read Sec 7 and Sec 8.

View (as seen on the Video link, too)

Difference quotient (DQ) and the definition of derivative

Finding derivative with DQ, Ex 1

Finding derivative with DQ, Ex 2

Do Take-home 1

You may use the reading and notes (but *not* a friend/classmate)

Also, do Sec 7 p 72 #1

**Wed Sept 13** Do Sec 7 p 72 #2, 3 a-d

Read "The derivative function and marginal analysis (of cost, revenue and profit)"

Due tomorrow, worked *independently*, same take-home with correction (lim of the DQ as h—>0)

View Shortcuts to the Derivative

Finding equation of tangent line to the curve

**Thurs Sept 14** Do Sec 8 p 78 #1, 2, 3, 4* using the derivative formulas* .

**Fri-Sun Sept 15-17**

1. Preview Sec 9 (continuity) with the videos at Videos on *Continuity*

2. Carefully look over worked solutions of today's handout *only to end of p. 207* (omit Marginal Average phenomena): "The derivative function and marginal analysis (of cost, revenue and profit)"

3. Read Sec 9. View all three Videos on *Continuity* See if you can do some on pp 84-85 #1 a-e, 2 a-d, 4, 5, 6. I have posted the solutions.

HOMEWORK FOR WEEK 5

**Mon Sept 18** SHORT quiz Wednesday on derivative rules and finding equation of the tangent line to a curve at a point.

Read (again?) Sec 10 (product, quotient, and exponential rules) and Sec 11 (chain rule).

Do Derivative extra practice handed out today in class. Refer to the Essential formulas handout

The first 10 extra practice are forms we covered. The others entail product and quotient rules. You can do them after watching again:

In the book, do Sec 10 #1-6, #8-10, 11, 12, 13.

Sec 11 #1, 2 b c f g l m, 3 a-d, f l m n, #4 a, #6

Did you try the continuity problems? We will spend 15 minutes on them next class.

**Wed-Sun Sept 20-24** Finish up Sec 9, 10 and 11 problems. Adding Sec 10 #1-6, #8-10, 11, 12, 13.

Do rest of problems on Derivative Practice handout; do Chain Rule handout problems. Skip trig examples.

For help, go to the Videos link and scroll down to for videos of clear, intermediate level examples.

Speed quiz on derivatives on Monday including all rules, with NO Essential formulas handout

HOMEWORK FOR WEEK 6

**Mon-Tues Sept 25-26** Be ready with questions to ask on Wed for Exam 1, which is Thursday Sept 28.

The following items will help you prepare.

And from previous semesters:

Domain limit and linear cost revenue profit analysis quiz

And a brand new practice problem of Cost Revenue Profit analysis

**Wed Sept 27** Study for Exam 1 to cover all topics Sec 1-11.

**Format** About 6 questions of several parts, including domain, limit, derivatives, and piecewise function continuity question, a cost revenue profit problem with interpretations, compound interest to find principal and final values, and solve for time to increase an investment (like time to double or get to some other future value).

**Thurs-Fri Sept 28-29** Read Secs 12-13. View (twice would be best) Implicit differentiation (ID). See my synopsis of ID method Video page.

Do problems in Sec 12 p 107 #2, 4, 5; and Sec 13 #1, 2, 3, 4, 8

HOMEWORK FOR WEEK 7

**Mon-Tues Oct 2-3** Read Sec 14 (related rates) and view related rate videos (read my synopsis on Video page).

Related rates 1: Area of circle and changing radius rate

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

Related rates 3: Ladder sliding down the wall problem

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

**Thurs Oct 5** Read Sec 15. Watch Extrema and Critical numbers as well as Increasing and decreasing functions

**Fri-Sun Oct 6-8** Do pp 129-130 #2, 4 a-i

HOMEWORK FOR WEEK 8

**Mon-Tues Oct 9-10**

View Finding critical numbers of a fcn

Second derivative test and concavity

Read Sec 17 and Sec 18.

Do Sec 17, p 141 #1, 2 a-m

The first part of Summary of Secs 15, 17, 18 will be a help.

**Wed Oct 11** Continue reading Sec 17 and work on finding intervals where f(x) is increasing or decreasing by checking test values in the intervals created by the critical numbers.

To hand in on *Thurs* Revised related rates quiz

**Thurs Oct 12** Read Sec 18; Do, in this order, #1, 3 a-e, 2 a, b, e, f, h

**Fri-Tues Oct 13-17 Fall Break** Read Secs 16, 19-21. View short videos on Sec 16 theorems

Catch up on the HW problems whose solutions I have already posted.

Homework for Week 9

**Wed Oct 18 ** Do Sec 16 p 136 #1, 2 and Sec 22 p 185 #3 a

Study for quiz on sketching a polynomial; see polynomial example in class notes Unit on graphing

View: Detailed examples of using first and second derivative to graph function View:

Graphing a simple rational function

Graphing a harder rational function

**Thurs Oct 19** View:

Sketching a more involved rational fcn with FDT and SDT

Limits at infinity, which relate to horizontal asymptotes (including "tricks" at 6:16)

Do Sec 19 #1 a b c, #2 a b c d f i

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

Sec 21 p 174 # 1, 2, 3

Sec 22 p 185 #4-8 (revisiting absolute min/max with business type questions)

Homework for Week 10

**Mon-Tues Oct 23-24**

FOCUS for Exam 2 The test will cover (perhaps not all of these, however):

- Short answer implicit differentiation; short answer concerning basic theory of critical points and inflection points (think of the Summary handout); finding the equation(s) of tangent(s) to a curve at a given x (you may use y instead of dy/dx);

- Related rate of a business type problem;

- Identifying critical numbers of various functions (short answer, not to graph);

- Graphing a rational function that involves HA and VA and showing that the FDT supports where it is increasing and/or decreasing and its concavity story;

- Business-type problem for max and min; an absolute max/min problem;

- Identifying a value of c where f'© is in agreement with the statement of the Mean value Theorem.

Here is a Supplementary problems with solutions for Sec 16. Look at these, especially #3 a b c and #4.

Scroll down on pdf to see the answers. To show the hypotheses of the MVT hold, you need continuity and differentiability on the stated interval (i.e., no issues with the function's domain on the interval named, and the function is smooth on the interval; all root, exponential, polynomial, and rational functions are differentiable on their domains).

Here is a video of A related rates problem in business

**Thurs Oct 26** Read Sec 23 and Alternate textbook section on optimization (intro)

View:

Optimization problem (instructive)

**Fri-Sun Oct 27-29** Do Sec 23 p 192 #2-5, 6, 9, 10, 12, 15, 16

Read Sec 26 (Functions of Two Variables)

Homework for Week 11

**Mon-Tues Oct 30-31** On the Videos page, where you can also see my (helpful, I hope) synopses, view:

Optimizing revenue given two points of data

Then go back and see if the Sec 23 p 192 problems are easier.

Read Sec 26 and do p 212 #1-4, #6-8.

**Wed Nov 1** Read Sec 27 (Partial Derivatives) and view Partial derivatives

For the next quiz I may take some problems from Alternate textbook optimization

Do Sec 27 p 219 #1 a b c e f i

**Thurs Nov 2** Read Sec 28 (Local Extremes and Saddle Points in 3-space)

DON'T IGNORE THIS VIDEO: For Sec 28 Local extremes and saddle points of multivariate function

**Fri-Sun Nov 3-5**

See the video page summary notes that go with these for weekend viewing:

Critical points and second derivative test for local max and min of multi-variable function f(x,y)

Read Summary Sec 28 Part I and Part II

The last four pages of the second pdf contain the book's Ex 28.3, with all those cases for finding critical points when the partials yield a system of equations in x and y. It's basically a step-by-step explanation of how to check for solutions and if necessary discard ones that don't work.

Do Sec 28 Problems p 226 #1 a-e, i, 2

Study for Mini-Quiz on partial differentiation and optimization (business problem).

Revised alternate text optimization

Homework for Week 12

**Mon Nov 6** Read Sec 29. View Optimization via Lagrange multiplier

**Wed Nov 8** The problems from Monday were a day soon. Now do problems p 233 #2 a b c e, 4, 6, 7

Do Take-home quiz on SDT for multi-variable functions f(x, y)

**Thurs Nov 9** Catch up on Sec 29 p 233 #2 a b c e, 4, 6, 7

Read Sec 24 Elasticity of Demand. See also my Summary of Price Elasticity of Demand

View Elasticity of Demand, a very good lecture.

Try to do the Sec 24 problems p 199 #1-9

**Fri-Sun Nov 10-12** Finish the Sec 24 problems.

Prepare questions for review day on Monday. We will also conclude elasticity on Exam 3 will be Wed Nov 6.

**Mon Nov 13** STUDY.

**Wed-Thurs Nov 15-16** Read Sec 30 and watch Antiderivatives and indefinite integration

First examples of antidifferentiation

Know all the rules for anti-differentiation on p 237-238 (basically the same as the video examples).

View: Examples of basic indefinite integration

Finding a particular F(x), given initial conditions (xo, yo)

Do p 242 #1 a-i

**Fri-Sun Nov 17-19** Do Antiderivative rules and practice

with plenty of examples, practice and answers.

Note this pdf's 6th rule, where it generalizes the antiderivative of e^kx. We will treat this in Sec 31 under u-substitution, but as a rule, this one is excellent to know as it saves time and is not hard.

Read Sec 31. View u-substitution

**Mon-Sun Nov 20-26** First, problems in u-substitution: Do Sec 31 p 248 #1 a b c e f g i j k l

Read ahead on *the definite integral*. (Skipping integration by parts for now).

By this we simply mean evaluating an integral on a closed interval. The answer is a number, not a function.

Read Sec 33. View Definition of definite integral

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

**Mon Nov 27** Read Sec 32. View Integration by parts

Do Sec 32 p 255 #1 a b c d e g h i k (see video and examples in text)

View Fundamental Theorem of Calculus

**Wed Nov 29** NEW POSTING:

First, Basic lecture on definite integral. It doesn't go into FTC (fundamental thm).

British man explaining the difference between indefinite and definite integral

Entire straightforward website on integration

View Finding area between two curves

Read Sec 34; do p 268 #1 a b e f, 4, 5, 6 a c g, 8, 9

Complete problems in Summary of antiderivative rules, practice problems

Start to prepare for the SKILLS TEST on Mon Dec 4

The skills test will include (though not necessarily be limited to):

Short answer items on finding a limit, derivative, implicit differentiation and equation of line tangent to a curve at a point, partial derivatives, integration, basic function sketches, finding intercepts of functions (x and y), TRUE/ FALSE that tests understanding of increasing, decreasing, concavity, inflection, marginality, interest (compound interest formulas), doubling time, elasticity.

**Thurs-Fri Nov 30-Dec 1** 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*, say cost fcn, value fcn, any quantity given a rate of change of that quantity. If we take the antiderivative of a marginal fcn we get back the total value of the function. (It's undoing the derivative through the antiderivative to get the sought after function.

*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 difference from the Sec 5 topic is now we consider a continuous flow of money (an income stream, like an investment or a business venture).

Do p 278, all. Solutions posted for #1 a, d, 2, 4 a, 6-9, 11, 12, 15.

**Fri-Mon Dec 1-4 ** Continue Sec 35 and catch up on older HW for the integration unit.

Skills Test is Monday.

**Mon-Tues Dec 4-6**

1. I put this off till the Skills Test was done. Do Sec 34 Take home quiz, due Wednesday

As usual, use notes but not friends and tutors.

2. View this final collection of videos, the applications of the definite integral:

Finding area between two curves

Position, velocity and acceleration

Present and future value of a continuous income stream

3. Do what you can of p 278. Solutions posted for #1 a, d, 2, 4 a, 6-9, 11, 12, 15.

Here are some notes I had from last semester. I don't care for the first two pages, so skip them. The rest are fine! 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).

**Wed Dec 6** Finish up anything in Sec 35 problems on p 278 you didn't get before today's lecture.

**Thurs Dec 7** Here is the Integration Unit Summary

people/mckenzie/math_220_hw.txt · Last modified: 2017/12/07 19:23 by mckenzie

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