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people:mckenzie:math_220_hw

Scan of Chapters 1, 2, 3 of our text

The date (in bold) refers to the day the assignment is given, not when it is due.

Doing homework daily (making an honest effort and using anything at your disposal) is the only way to succeed in the course. I will occasionally collect a set of problems, which I will announce ahead of time. Usually, though, a collected assignment is a separate problem I hand out.

**Week 1**

**Tues-Wed Jan 16-17** Read Sec 1 and Sec 2; problems Ch 1, p 5, #1, 2, 7, 8; problems Ch 2, pp 15-16, #1-13

Study your notes on graph sketches to know.

The math 220 Video page is mainly for calculus. But, if you need to brush up on exponents and radicals, or on domain of a function, check out Math 108 video link. The first couple of links there are for exponents and radicals. Scroll down a little way to find the link for finding domain of a function.

**Fri-weekend Jan 19-21 ** Read Sec 3 and Sec 4; do problems Sec 3, pp 26-27

View Break even problem 1, Break even problem 2

Go to SUPPLEMENTAL MATERIALS and do Worksheets 3, 4, and 8 (exercise 1 only) for more practice on exponents, domain and composition of functions.

**Week 2**

**Mon Jan 22** Here are thumbnails of the Essential function sketches. The last several all a little faint. I will repost some day.

Finish Sec 3 problems if you have not done so.

Read Sec 4 again. View these helpful videos:

Solving exponential equations without and with logs

Examples of solving exponential equations

Example solving logarithmic equations

Another example solving logarithmic equations

Try to do these before lecture. 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

**Tues Jan 23** The main skills needed are solving for the variable (say, t) when it is in an exponent. All attendant properties of exps and logs that are needed.

*Read Sec 5 Compound Interest*

Understanding the number e (exponential growth).

Compound interest, present and future value problems

**Wed-Thurs Jan 24-25** Do Sec 5 problems p 57 #1-7 ONLY!

Here's a Summary of log and exp properties, the new handout

And here is the summary of Sec 5, today's Lecture on compound interest

**Fri/weekend Jan 26-28** Study for Quiz 1. See Summary Sections 1-5

Read Sec 6. View the following intro video on limits.

Then go to Videos to view first 6 Limits videos.

After looking at the videos and the examples in the reading, do p. 67 #1-12, #16-30 even.

**Week 3**

Heads up: Our first exam is Wednesday Feb 7. It covers Sec 1-9.

New HW:

**Mon Jan 30** Finish Sec 6, p 67 problems. (HW Solutions are posted.)

Read Sec 7. Go to **Derviatives** 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)*

**Tues Jan 30** Do Sec 7 p 72 #1, 2, 3 a-d

Read Sec 8 and view Finding equation of tangent line to the curve

Also, check out the

Sec 8 p 78 #1, 2, 3, 4* using the derivative formulas*

**Wed-Thurs Jan 31-Feb 1** Read "The derivative function and marginal analysis (of cost, revenue and profit)"

Read Sec 9. View all three Videos on *Continuity*

Short quiz on Friday on Limits!

**Fri-Sun Feb 2-4** Do Sec 9 pp 84-85 #1 a-e, 2 a-d, 4, 5, 6

Study *only to end of p. 207* "The derivative function and marginal analysis (of cost, revenue and profit)". This is a reading from an alternate text.

Week 4

**Mon-Tues Feb 5-6** Study for Exam 1, Sections 1-9.

FOCUS PROBLEMS:

Besides HW problems, these, which will put you in a good place for the next unit as well. We can't test everything on every test, but eventually you see something from all the concepts and skills. See SUPPLEMENTAL MATERIALS for worksheets named below:

Sec 1-3. Domain, C, R, P linear functions, interval notation

Supplemental Worksheet 2 Exercise 3

Supplemental Worksheet 1, Exercises 1, 2, 3

Supplemental Worksheet 4, Exercise 1c, d, f, 2a-f

p. 28 #4 a-g, #6-14

Sec 4. Logs and exps

p. 43 #4, 58 e, f, g

Sec 5. Compound interest formulas; approx value of e

Supplemental Worksheet 7 Exercises 1, 2, D1-D4, D6, D7

Sec 6. Limits: In the reading Examples 6.2, 6.3, 6.4, theorem on p 63 on properties of limits; Examples 6.8, 6.9, 6.12, 6.13

Supplemental Worksheet 10/11 Exercises 1, 2, 4, 5

Sec 7 and 8: Derivative (Slope of tangent to a curve)

Supplemental Worksheet 13, Exercise 21, 3a, 3b

Supplemental Worksheet 8 Exercises 4d, 4

Topics: domain of a function (use interval notation); limits; continuity; linear cost, revenue, profit problem; compound interest problem; find derivative using limit of DQ process; find equation of line tangent to function at given point.

**Wed-Thurs Feb 7-8** Read Sec 10 and view relevant videos.

Read again Sec 10 (product, quotient, and exponential rules).

Read Sec 11 (chain rule).

**Fri-Sun Feb 9-11** Do Derivative extra practice. #18 and #20 on this sheet might bother you a little.

Refer to the Essential formulas handout and the videos:

You should be able to start problems in Sec 10: #1-6, 8-10, 11, 12, 13

WEEK 5

**Mon Feb 12** Do Sec 10 problems #1-6, 8-10, 11-13

Read Sec 11, Chain Rule.

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

See the Essential formulas handout

**Tues Feb 13** I drew on these videos for my worked applications today of Marginal cost, revenue, profit: Ex 1

and Ex 2

Sec 11 problems on chain rule: #1, 2 b c f g l m, 3 a-d, f l m n, 4 a, 6

Handout given in class today (Cost Revenue Profit analysis), to be collected Friday.

Read Sec. 12.

**Wed-Thurs Feb 14-15** Study problems in Sec 10 and 11, for Friday quiz on derivative rules and chain rule. Good questions to study are those on
Derivative extra practice, though it lacks practice of log function differentiation and chain rule.

**Fri-Sun Feb 16-18** Read Sec 12 and Sec 13.

Do Sec 12 problems on d/dx notation: p 107 #2, 4, 5.

See my synopsis of Implicit Differentiation (ID) on the video page and watch the video there.

WEEK 6

**Mon Feb 19** Do Sec 13 #1, 2, 3, 4, 8. Solutions posted simultaneous to assignment.

View related rate videos (but first and then after, 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

Here is a video of A related rates problem in business

Read corresponding section, Sec 14.

**Tues Feb 20** Do Sec 14 pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14

**Wed-Sun Feb 21-25** Read Sec 15.

View Extrema

Critical numbers of a function and an excellent example to illustrate

More about the excellent example in previous video

Patrick mjt finds critical numbers of a fcn

Patrick mjt does a harder example

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

WEEK 7

**Mon-Tues Feb 26-27** Study Sections 10-15 for Exam 2, this Wednesday.

WEEKS 8 & 9

**Thurs March 8** View Increasing and decreasing functions

Second derivative test and concavity

Read Sec 17 and Sec 18.

**Fri-Sun March 9-11** Read Summary of Secs 15, 17, 18

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

Study for Tuesday QUIZ on using critical numbers and FDT on f(x) to find intervals of increasing/decreasing

**Mon March 12** For the following video, pay close attention to what the teacher says at 3:45 onward in terms of creating the curve above the number line. He draws an actual rough sketch of the function!

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

Also, see the Alternate text 'Applications of Differentiation Part 1 FDT

'Applications of Differentiation Part 2 SDT

And, my Summary of Secs 15, 17, 18 noted on Friday is a concise overview, but for examples, the alternate text and the videos are the best.

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

**Tues March 13** Make sure you have done Sec 18 by now.

View: Graphing a simple rational function

Graphing a harder rational function

**Wed-Thurs Mar 14-15** 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-Sun Mar 16-18** 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

Read Sec 22, absolute extreme.

WEEK 10

**Mon March 19** Do Sec 22 p 185 #3-8

To hand in Wed: p 168 #5i and p 174 #6 (NOTE THE CHANGE)

**Show all work as needed** to give: Domain, intercepts, any VA and HA, critical numbers and potential POI, sign analysis to support intervals of increasing, decreasing concave up, concave down; determine any local max and min and POI and value of the fcn at these points.

Make a NICE sketch, clearly indicating all the features you found.

Read Sec 23 optimization

**Tues March 20** Complete the absolute max/min hw.

Read Last semester notes on Optimization. (The pdf of alternate text isn't uploading. Troubleshooting!)

View: Optimization problem (instructive)

**Wed-Thurs March 21-22** Go to Videos page, where you can also see my (helpful, I hope) synopses of optimization. View:

Optimizing revenue given two points of data

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

**Fri-Sun March 23-25** Read Sec 26 (Functions of Two Variables).

Catch up on all optimization homework.

See Opt. worksheet from Supplemental Materials, too, for extra problems.

Read Sec 24 Elasticity! (Change of schedule )

View Elasticity of Demand, a very good video lecture.

WEEK 11

**Mon March 26** See also my summary: Price Elasticity of Demand

Do the Sec 24 p 199 #1-9.

**Tues March 27** Finish Sec 24 problems. No quiz tomorrow, but there will be a take-home comprehensive over the break.

View Multivariable functions up to 9:45

Read Sec 26 (notation of z = f(x,y); do Sec 26 p 212 #1-4, #6-8

Read Sec 27 (Partial Derivatives)

View Partial derivatives up to 11:07

**Wed-Sun March 28-April 8** This homework takes you through the break.

View rest of Partial derivatives

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

Do the Take-home quiz on Optimization, Elasticity, Optimization and Partial Derivatives

Read Sec 29. View Optimization via Lagrange multiplier

Week 12

**Mon April 9-Wed April 11** Do problems Sec 29 p 233 #2 a b c e, 4, 6, 7

Wednesday April 11 is a review day for Exam 3. Exam topics come from Sec 18-24, 26, 27, 29:

Curve sketching (polynomials), optimization (Sec 23), elasticity, multivariable functions, partial differentiation, Lagrange multiplier method of optimization (Sec 29). Also, concepts of absolute vs local extrema.

Note that the Supplemental Materials for Sec 29 are basically the book's problems!

**Friday-Sunday April 13-15** Focus problems for Exam 3:

When curve sketching, keep an eye on the methodical way you find the roots of the derivatives and inspect for intervals of increase, decrease, concave up, concave down, CP and POI.

Sec 19 p 152 # 2c, e, f, g, h

Sec 20 Save this for the FINAL

Sec 21 p 174 #5, 6, 7

Sec 22 p 185 #3 a, c, d, 5, 6

Sec 23 p 190-191 Ex 23.3, Ex 23.5, p 192-193 #4, 9, 10, 12, 13, 16

(Saving geometry-based problems for the FINAL)

Sec 24 p 197 Ex 24.1, 24.2 p 199-200 #4-9

KNOW BOTH FORMULAS E(p) and R'(p) and how they relate to one another.

Sec 26 This is the notation and meaning of multi-variable functions, in which there is more than one independent variable. You apprehend the meaning of the notation of f(x,y,lambda) with this (or C(x, y, z) or any other multi-variable function).

pp 212-213 #5-8

Sec 27 p 216-218 All the examples in the reading, if you are still uncertain. We prefer the spare notation to the Leibniz notation.

p 219 # 1, 2

Sec 28 Skipped this semester. Finding local extrema of surfaces in 3-space.

Sec 29 pp 229-231 Ex. 29.2, Ex. 29.3, pp 233-234 #1-4, 6

WEEK 13

**Mon-Thurs April 16-19** *Revised schedule of HW for this week.*

By Friday's class you should have *read through Sec 31* and watched the videos through u-substitution.

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

Antiderivatives and indefinite integration

Examples of basic indefinite integration

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

Finish Sec 30 p 242 *All problems.*

Read Sec 31

View both u-substitution

**Fri-Sun April 20-22** Re-read Sec 31 and watch last night's videos again.

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

Read Sec 32.

View Integration by parts

WEEK 14

**Mon April 23** Do Sec 32 p 255 #1 a b c d e g h i k (see video and rely on examples in text)

You will want to watch this again: Integration by parts

Read Sec 33. View the videos:

Fundamental Theorem of Calculus part I

Fundamental Theorem of Calculus part II (the definite integral)

Example 1 of finding a definite integral

Example 2 of finding a definite integral

Go back and look Videos for Sec 30, 31, 32.

Other good ones are found at SUPPLEMENTAL MATERIALS

This site needs some curating for expired links. But most are active.

**Wed-Thurs April 25-26** The following was supposed to be assigned last night.

Read Sec 33. Do p 260 #1 a-e i j k o p q

My notes on last semester on finding the definite integral.

British man explaining the difference between indefinite and definite integral

Patrick explains Riemann Sum to approx area under curve on interval [a,b]

Patrick defines definite integral via Riemann Sum

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

WEEK 15

**Fri-Sun April 27-29** Riemann sum calculation: As assigned last week, to hand in Monday:

On the interval [1, 6], find the approximate area under f(x) = x + 4 using a Riemann sum of 8 rectangles fitted under the curve. This means the left endpoint of the rectangle meets the function to be the height of the rectangle.

Compare your answer to the actual area, which you should also find.

Read Sec 35 and get to work on p 278, all. But first, consider that we've covered the first half of this very DENSE section. It covers far more than the title suggests. It's all about accumulation. Here is a road map:

*Riemann sum*The sum of areas of rectangles fitted under/over f(x) on [a, b] approximates area under f(x) as n (no. of rects) increases. Limit of this sum as n –> inf = definite integral on [a, b].

*Average value of a function*The average value f(x) attains on [a, b] calculated by definite integral divided (b - a), the width of the interval.

*Total value of a function over time t*Cost, stock value, displacement, etc. The area under a rate function f'(t) is the value of f(t) over time t.

*Present and future value of an investment through a constant flow of money*Analogous case to the Sec 5 topic of present and future value of a one-time investment). But in Sec 35 we consider a continuous flow of money (or income stream, like an investment or income from a business venture) over time.

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

**Mon-Wed April 30-May 2** Finish up Sec 35 problems p 278, and the supplemental materials (handouts)

**Thursday May 3** Exam 4 is tomorrow!

*FOCUS QUESTIONS FOR EXAM 4*

Sections 30, 31, 33, 34, 35:

Example problems in the text: The worked examples in the reading are VERY IMPORTANT.

Additionally:

Sec 30 #1 all, #3, # 6, 8

Sec 31 #1 e, g, h, i, j, k, m, #3, #4

Sec 32 #1 b, d, e, g, h, i, j

Sec 33 #1 b, c, e, f, i, j, k, l, o

Sec 34 #1 all of these are good practice of basic definite integrals.

By the way, these give the 'signed area', rather than the total area enclosed. When a function crosses the x-axis, the part below ends up having a 'negative area'.

#4, #5, #6 d, f, g

Now you have to examine where the graph crosses the axis or where two graphs cross and look at the total area enclosed, not net area. This can entail breaking up the integral into two parts.

Sec 35 #1d, d, #2, #5, #7, #11, #12, #14, #15

people/mckenzie/math_220_hw.txt · Last modified: 2018/05/03 14:47 by mckenzie

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