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people:mckenzie:math_220_hw

Scan of Chapters 1, 2, 3 of our text

The day (Mon, Tues, etc.) refers to the day the assignment is given, not when it is “due.”

By “due” I mean you should have done it and have questions ready for me. If you don't, then I move on.

Making an honest effort daily to do HW is the only way to pass the course. Occasionally, I collect a set of problems. Often, a collected assignment is a hand out or take-home quiz.

WEEK 1 (AUG 22-24) Your progress should be, roughly, 3 lines a day.

Read Sec 1 and Sec 2; view first five videos at SUPPLEMENTAL MATERIALS

Further review: Simplifying radicals with constants only

With variables

Many videos on negative exponents

Do exercises: p. 5 #1, 2, 7 (first two, and for enrichment the third an fourth), 8

View: Finding domain of a function

Do pp 15-16, #1 (domain), 2 (domain and roots–set the fcn = 0 and solve), 8, 9, 11, 12, 13

WEEK 2 (AUG 27-31)

Mon Read Sec 3 and Sec 4

View Graphing piecwise functions

View Break even problem 1, Break even problem 2

Do exercises Sec 3, pp 26-27

8-O REVISED Tues/Wed/Thurs 8-O

Quiz topics to study for Friday Quiz Sec 1-3

Accurate sketches of essential functions showing intercepts and asymptotes; finding natural domain of a function; function composition; accurate sketches of a piecewise function and expressing its stated domain in interval notation; solving an equation for x (reference Ex 2.5 and 2.6); multi-part problem on cost, revenue and profit, as done in class today; definition (what is meant by) marginal cost for any cost function.

Read Sec 6, Limits. Watch the videos by Patrick. He is among my favorite Internet teachers for his ability to simply and clearly convey the lesson.

Basic ideas of limits

Evaluate limits using properties, Ex 1 and Ex 2

Fri-Sun Do p. 67 #1-12, #16-30 even. Numerous examples are found in the reading and in the rest of the videos under LIMITS at Videos. Here they are, as well.

Finding limits from a graph (This is one of his rougher videos, but well explained.)

Evaluate limits using properties, Ex 1

Evaluate limits using properties, Ex 2

More techniques for evaluating limits, Ex 3 (gives a little jump on continuity)

Ex 4 involving radicals

Ex 5 also with radicals

8-O IMPORTANT Infinite limits in which a function goes to positive infinity or negative infinity as x approaches a:

Ex 6 (involving rational expressions)

Read Sec 7 and Sec 8.

Go to Derivatives section of Videos, read my intro there and watch the videos under the first section, Instantaneous rate of change of a function at point via the difference quotient (DQ)

WEEK 3 (Sept 3-7)

Tues Finish Sec 6 Exercises #1-30, on p 66. See my posted solutions!

Re-read sec 7 & 8

View Derivative videos: Difference quotient (DQ) and the definition of derivative

Finding derivative with DQ, Ex 1 and Finding derivative with DQ, Ex 2

Wed Do Sec 7 p 71 #1, 2, 3 a-d

8-) HAND IN ON FRIDAY the worksheet we started in class. Here it is again, with typo fixed:

Take home 1

I opened up the spacing, so you can do a nice neat job on this.

Fri View Shortcuts to the Derivative and Finding equation of tangent line to the curve

8-O Read again "The derivative function and marginal analysis (of cost, revenue and profit)". This pdf is from a text that has many applications. Its approach is methodical and clear. Especially note the approximation of exact cost to producing an additional unit to the marginal cost, C'(x). For our purposes, we use C'(x) as this cost to produce and additional unit.

Rosh Hashana break homework

View enough of these to attain the skill for finding equation of the line tangent to f(x) at a given point:

Ex 1, Ex 2, Ex 3, Ex 4

Do Sec 8 p 78 #1, 2, 3, 4, 7 using power rule rather than limit definition to get f'(x) WEEK 4 (Sept 12-14)

Wed 8-O Study for SHORT Friday quiz: limit computation, equation of line tangent to f(x) (using power rule), and derivative computation. NO finding derivative via limit of DQ as h –> 0.

Read Sec 10 (product, quotient, log and exponential rules of differentiation).

View Product rule examples and Quotient rule examples and other videos under Differentiation in Videos.

Do Sec 10 pp 91-92 #3-6, #8-13. See example videos for product, quotient rules under “Derivatives”

Fri-Sun Catch up on Sec 10 exercises (see previous line).

Read Sec 11 (chain rule). View Chain rule proof

This is a pretty good video. The lecturer uses the Leibniz notation dy/dx. There's a little fudging of u(x) as g(x), but he says so. Chain rule is an ESSENTIAL skill. Most problems involve chain rule.

We did the exp and log base e derivative rules, but not the ones for bases other than e. They are similar but have an extra multiplier term. Here are two simple short videos that show examples of just what the book and the handout have:

Derivative of an exponential fcn with base a

Derivative of a log fcn with base a

See Videos for examples of working chain rule.

Do pp 96-Sec 11 #1, 2 b c f g l m, 3 a-d, f l m n, #4 a d e #6, 7

Read Sec 12, Higher Order Derivatives and Leibniz notation (dy/dx)

WEEK 5 Sept 17-21

Mon Do Sec 12 problems on Leibniz' dy/dx notation: p 107 #1 only.

Do Chain rule worksheet. Exercise 2 says decompose the function into f(u) and u(x). Please take the derivative dy/dx = (dy/du)(du/dx), too!

See my synopsis and watch video of Implicit Differentiation (ID) in Videos

Read Sec 13.

Tues/Wed Check your answers from the Chain Rule worksheet on:

Solutions to Chain Rule worksheet

:!: Catch up on differentiation HW :!:

View related rates videos; read synopsis Video page

Thurs 8-O PRINT AND READ this PDF on Sec 13/14

Fri Do Sec 13 #1, 2 a-d, 5, 6, 8; do Sec 14 pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14

STUDY FOR QUIZ ON MONDAY for SEC 01 (8:00 a.m.) class, TUESDAY for Sec 02 class

Catch up on all HW and have questions ready to review before next week's exam.

WEEK 6 This week you have EXAM 1 on Friday, covering Secs. 1-4, 6-8, 10-14

Omitted for now are Sec 5 (compound interest) and Sec 9 (continuity)

Mon/Tues Here is a link to Class notes by NS

Finish the Related Rates HW in Sec 14, now that you have had the lecture. Use the pdf too!

8-O Focused List of Exam 1 Topics

1 Domain of function. Use interval notation. Found y intercept and roots.

2 Limits requiring algebra and not.

3 Log and exponential properties and graphs we often discussed in service of understanding limits and in simplifying derivatives.

4 Cost revenue profit break even analysis

5 Differentiation like on the quiz. We'll go over in class tomorrow.

6 Implicit differentiation to find equation of tangent line to a curve in x and y.

7 Demand equation and revenue and marginal analysis; p(q) or q(p) type

8. Related rates of a business themed problem. The scheme is the same idea of getting at rate of change of y through rate of change of x: dy/dt=(dy/dx)(dx/dt)

Wed EXAM 1 PREP:

1. Deriv quiz key Sec 01 and Deriv quiz key Sec 02

2. Covered mostly in first class, an RR problem from text not previously assigned, p 121, a good, thinking, question. It required three scans from the small machine:

#13a, #13b, #13c

3. From reading and exercises, study and work these through to the extent that you get it. Important to get to the end rather than do every bit. For the purpose of completeness, I've been thorough, a little repetitive. In italics, see extra derivative practice not previously assigned.

Sec 2: Foundations. Look esp. at Ex 2.5.1-4

p 15 #1 a-d, f, 2 a-d

Sec 3: Foundations. Look esp. at bottom of p 22 to p 25, Ex 3.5

pp 26-27 #10-13

Sec 4: More foundations, more to be addressed fresh in next unit. For now: Log Def p 34, Exs. on p 35, graph & features of exp and log fcns on p 36, Props 1 & 2 on p 36

pp 42-43 #1-5, 10-12

Sec 6: Ex 6.2-6.4, Thm p 62, Ex 6.11

p 66 #1-11, 19-21, 24, 27, 29 (good factoring practice)

Sec 7-8: See HW problems, using power rule, not lim of DH as h –> 0

Sec 10: #3-6, 10, 11

Extra derivative practice not previously assigned: #16 a-d, g, j, m, m, o

Sec 11: Ex 11.6, 11.7

pp 96-97 #2 a-h, 3 a-f, k-m, o, 6, 7

Extra derivative practice not previously assigned: #13 a-m (but SKIP d, e, h, l)

Sec 12: Continues Sec 11, but using

Ex. 12.2, 12.3 [You're set on this. It's used to best effect in Sec 13 & 14]

Sec 13: #2 a b c, 3-5

Sec 14: Ex 14.1, 14.2 (basic geometry, touches on business applications), Ex 14.4

pp 120-12 #1, 2, 4, 6, 9, 12, 133 (see solution at top of today's list)

On PDF on Sec 13/14:

pp 211-215, Exs. 3, 6, Box on solving ID p 212

Circled word problems at end of PDF.

WEEK 7

Mon Read rest of Sec 4 pp 38-41.

View:

Using change of base formula

Solving exponential equations without and with logs

Examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

EXERCISES:

Basic log property (you might have done these a while back): pp 43-44 #1-5, 8 b e f g, 10 a c e f, 11 e f h, 12

Cancellation and change of base properties: pp 44-45 #14, 18, 19

8-O The important conclusion: Solving log equations p 44 #20 a-e, 21 b d f

Tues Read Sec 5. Notice you will use solving exponential eqns through log properties to do this chapter.

Wed View Where does e come from?

Understanding the number e (exponential growth) At 3:30 he gets to the point of compound interest, but the video is worth watching beginning to end.

Compound interest, present and future value problems Mr Tarrou gives kind of goofy longer examples, but he's clear and his examples are valuable.

Read; suggest you print for reference Summary of compound interest. It gives a sequential explanation leading to the formulas.

Do Sec 5 problems pp 56-57 #1-7 and the Supplemental Materials Worksheet on compound interest

8-) Mini quiz in class Friday on solving exp equations. We'll exchange papers and mark it right away!

Fri Finish up Sec 5 problems including worksheet.

If you're shaky on exponential operations (esp base e, essential for calculus), then do the extra set of exponential practice problems on p 57 or thereabout.

Read Sec 9, Continuity. View the Continuity videos at Videos.

WEEK 8

Mon Review graphing piecewise functions

Read Sec 9 again and do pp 83-84, #1-9

Tues (This includes the Monday class). Read Secs 15 & 17.

View Extrema

Critical numbers of a function and an excellent example

More about the excellent example

Patrick mjt finds critical numbers of a fcn and A harder example

Do Sec 15 pp 129-130 #2, 4 a-i

Wed

8-O Fall Break Homework: I can't emphasize strongly enough how important it is for you to read Sec 17 & 18 (skip Sec 16) and view:

Increasing, decreasing functions

First derivative test

Second derivative test and concavity

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

Supplement your reading of section with the PDFs, Alternate text 'Applications of Differentiation Part 1 FDT and 'Applications of Differentiation Part 2 SDT

Read my Summary of Sections 15, 17, 18

WEEK 9

Mon Read Sec 18. View: Examples first and second derivative test to graph functions

Do Sec 18 (in this order) #1, 3 a-e, 2 a b e f h

8-) Now you have done all the calculus theory for the unit; the rest of the assignments build on it, adding ideas about polynomial and rational function sketching via precalculus you can remember.

Read Sec 19. View Graphing a polynomial

Tues 8-O Please note, in Sec 19 HW, skip #1 because the question is confusingly worded.

Do Sec 19 p 152 #2 a b c d e f h i

:-D The reading for Sec 20 is shortened to the following 3 sections:

pp 159-162 Examples 20.1-20.4

Last paragraph p 163 (“Not every limit…”) to p 164, Example 20.8

Last paragraph p 165 “Revisiting the number e” through p 166, the proof of the limit that gives e

Wed :-D The reading for Sec 21 is shortened to pp 171-172.

Do this Take home on curve sketching. Work independently!

I will desk check this take-home in all four sections this Friday, review day for Exam 2, Monday, Oct 22

Prepare questions for Exam 2 to ask in class Fri.

Thursday Have specific questions ready from topics in Textbook Sections 5 (compound interest), 9 (continuity, 15 (critical points, solving f'(x) = 0 for several types of functions), 17-21 (curve sketching through FDT, SDT, and precalculus techniques.

Friday Study for Exam 2, Monday Oct 22. Go back and watch videos for these topics.

Focus on Sec 5, #1, 2, 4, 5, 6

Sec 9 #1, 2 a b c, 4, 6

8-O You will be expected to know and demonstrate whether a function f(x) is continuous at x = a when it satisfies all three criteria: a in domain of f, RHL = LHL = L as x –> a (that is, the limit L exists as x approaches a), and f(a) = L.

Sec 15, 17-21 HW problems assigned therein, but especially as seen on the take-home. Concepts related to the first and second derivatives and how these are illustrated by various types of graphs

Also, I have posted NS's notes. See link on Math 220 main page

WEEK 10

Tues Even if you did not have class today, this section is no different than the previous max/min, except now you much check the endpoints of the closed intervals the function may be restricted to.

Read Sec 22. Do p 185 #3 all

Wed Do p 185 #4-8 (absolute min/max with business application questions)

Read Sec 23.

View optimization problems dealing with geometry:

Fence problem 1

Fence problem 2

Box problem

Fri View more optimization videos; and you can see Videos for notes about each.

Computer software sales with two examples, similar to lamp sales problem in the HW. (The y-intercept in the first example of the video is incorrect; it wouldn't be that n = 0 price reductions means $0 revenue–more about that in class).

The famous Hot dog problem

A slightly different approach (you can wait to watch this one till Monday): Optimizing revenue given two points of data

Do Sec 23 p 192 #2-5, 6, 9, 10, 12, 15, 16

There are plenty of opportunities to do more practice. The short excerpt from Alternate textbook on optimization has a good explanation and examples on pp 1-3, but the p 4 example is confusingly done. The problems on pp 5-6 are nice.

Here's a PDF of Various optimization problems from another textbook

WEEK 11

Mon 8-O Do Practice problems for optimization quiz to prepare for Wednesday

Read //Price Elasticity of Demand//

and also Sec 24, on Elasticity.

View Elasticity of Demand, a good video lecture.

Tues 8-O To hand in Wednesday, TAKE HOME QUIZ (rather than in-class):

#3, 5, 8 of Practice problems for optimization quiz

Wed Sec 24 exercises, p 199 #1-9

Fri Do Supp Mat'ls elasticity exercises on Elasticity worksheet

Sec 25-26: Though we won't graph z = f(x,y) (surfaces in 3-space), WATCH THIS VIDEO to see what is accomplished with partial derivatives:

Multivariable functions

The lecture is quite clear and helps you see what's going on with that third variable z.

Read Sec 26 (notation of z = f(x,y); do Sec 26 p 212 #1-8

8-O View Partial derivatives up to 11:07

Read Sec 27 (Partial Derivatives)

WEEK 12

Mon View rest of Partial derivatives

Read again Sec 27 and study text's examples. We prefer spare notation f sub x and f sub y to the Leibniz notation.

Do Sec 27 p 219 #1 a b c e f i, 2, 3, 4

Sec 28: Skip!

Tues Lagrange Method with Krista Ex 1 and Lagrange Method with Krista Ex 2

Read Sec 29. Especially pay attention to pp 229-231 Ex. 29.2, Ex. 29.3

Catch up on any previous HW exercises. I will post some PDF suggested examples from the two alternate texts.

8-) NO QUIZ ON WEDNESDAY (but HW desk check on Friday)

Wed Do pp 233-234 #1-4, 6, 7

Prepare questions to ask on in class to prepare for Exam 3, which will be on Monday Nov 12

Fri Study for Exam 3, Sections 22, 23, 24, 27, 29

See this space for some supplemental items from other sources to practice.

Solutions to Sec 29 and more on Sec 23 have been posted.

See also Unit 3 lecture notes by NS on the Math 220 page.

WEEK 13

Tues Read Sec 30 and view Antiderivatives and indefinite integration

Wed/Thurs Do Sec 30 p 242 All problems

Watch the first video again and this one, as well More antiderivative examples and graphical explanation!

Fri-Sun As a result of the SNOW DAY, the weekend assignment is revised. There are several essential videos.

Here's a good video on Initial value problems

Integrals of 1/x type

Read Sec 31 and Sec 32

WEEK 14 Includes THANKSGIVING BREAK HW

Mon-Fri Readings: Sec 32 and Sec 33 and corresponding sections in Chapter 4 of Bittinger text.

View Integration by u-substitution and Examples of u-substitution

Do Sec 31 p 248 #1 a b c e f g i j k l

If you have not had the Integration by Parts lecture, you may skip to Sec 33 and do Definite Integral problems after watching this excellent video with many BASIC examples up to 19:25:

First examples of finding a Definite Integral

And a short on by Krista for e^-2x:

Do Sec 33 p 260 #1 a-g

Further examples by Patrick:

Example 1 of finding a definite integral

Example 2 of finding a definite integral

Continuing with IBP (Integration by Parts), a challenging technique at first (the 8 a.m. class has not had the lecture, but are expected to view the video and read the chapter as well as the Bittinger reading)

Integration by parts--the basics, Mathispower4u

Integration by parts, Patrickmjt

Do Sec 32 p 255 #1 a b c d e g h i k

WEEK 15

First of all, go back to WEEK 14 and look at the videos again. Do Sec 32. I have posted the solutions so you may check yourself.

Mon-Tues Read the Bittinger PDF Ch 4, Sec 4.3, on the Definite Integral (which corresponds to our somewhat notorious Sec 33, whereas Bittinger is easier to understand and has more detail)

Do Sec 33 p 260 #1 a-g. I posted the solutions (that set happens to include some notes on Sec 34).

8-O Do this PRACTICE QUIZ for ;-) FRIDAY Integration Quiz 1 to cover Sections 30-33:

Integration Quiz 1 practice p. 1 and Integration Quiz 2 practice p. 2

Wed Here's the Integration chapter from Bittinger

And the Supp. Matls. wksht. definite integrals

Read Sec 34.

View Finding area between two curves

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

Please go ahead before Friday and watch the average value videos for Fri - Sun. Then rewatch them on the weekend.

Thurs-Sun Read Sec 35.

It is a DENSE section covering far more than the title suggests. I offer a road map, along with some summary PDFs later:

  • Riemann sum: The sum of the areas of an ever-increasing number of rectangles approaches the area under the curve, i.e., the definite integral;
  • Average value of a function: A neat idea. With it you can find the average value of a function on [a, b] by dividing the definite integral by the width of the interval.
  • Total value of a function: This is essentially why we do integration in any discipline. The definite integral of a rate fcn leads to the total value fcn.
  • Present and future value of an income stream: The analogous case to Sec 5 present and future value of a one-time investment. But now we consider a continuous flow of money rather than a one-time deposit at the start of the period. Business ventures entail income streams.

Here are the videos:

Finding area between two curves

Average value of a function

Present and future value of a continuous income stream

Supp. Matls. wksht. total & avg value of a fcn

Here is key to Practice Integration Quiz 1

When in doubt, look to Bittinger's Ch 4 Integration.

WEEK 16

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

Supp. Matls. wksht. present & future value of income stream

8-O Here is the Integration Quiz 2 practice with solutions

Tues/Wed Read through my Integration Unit Summary with Examples

Continue catching up on HW and see Bittinger PDF and other exercises.

Wed-Fri Prepare answers to problems in the

p 397-398 #54-57 (inital value problems), #59-67 odd (word problems on total value of a function)

p 407 #1-11 odd, p 422 #35, 37, 45 (signed area), p 423 #59-63 (more total value word problems)

p 434 #21-27 odd (area between functions) #39-43 odd (average value) #49-52 all (word problems average value)

p 443 and p 452 Exercise sets 4.5 and 4.6 ANY ODD PROBLEM INTEGRATION PRACTICE!

Many of the solutions are here : here

m( The Bittinger formulas for PV and FV look a little different from the development we see in the text and videos.

But the problems are pretty good. To prevent confusion, however, go to the supplemental worksheets for extra practice for now, as previously posted and here:

Supp. Matls. wksht. present & future value of income stream

Gotta go to work.

people/mckenzie/math_220_hw.txt · Last modified: 2018/12/09 15:09 by mckenzie