**Problem of the Week**

**Math Club**

**BUGCAT 2018**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

people:mckenzie:math_220_hw

Scan of Chapters 1, 2, 3 of our text

The assignment is given on the day named.

You should have questions for me and be ready to answer mine on the previous day's assignment.

Quizzes will be announced for the most part, about one per week.

Making an *honest* effort daily to do HW is the *only* way to pass the course. Sometimes I collect a few problems. Maybe a hand-out or a take-home quiz. Sometimes, I do a desk check during the lecture break.

WEEK 1

**Wed to Thurs**: Read Ch 1 and 2; view first five videos at SUPPLEMENTAL MATERIALS

Further review: Simplifying radicals with constants only, With variables and Many videos on negative exponents

Do p 5 exercises: #1, 2, 7, 8

View: Finding domain of a function

Do p 16 exercises: #9-15

**Fri-Sun** View Graphing piecewise functions; do rest of Ch 2 exercises, pp 15-16, #1-6

Read Ch 3; view Break even problem 1 and Break even problem 2

The first problems in Ch 3 cover the review of lines, whose *general* form is px + qy + r = 0.

Do Ch 3 p 26 exercises #1-5

WEEK 2

**Mon** At the VIDEOS link, view the first group of videos (Cost, Revenue, Profit)

Do rest of Ch 3 exercises pp 27-28 #6-16.

Read Ch 4 (Exponential and Logarithmic Functions)

View Graphing exponential fcns (up to minute 7:30) and Graphing log fcns

And Solving exp eqns, Solving log eqns Ex 1 and Ex 2, Using change of base formula

Do pp 43-44 #1-5, 8 b e f g, 10 a c e f, 11 e f h, 12, 14, 18, 19, 20 a-e, 21 b d f

**Wed** Read Ch 5

At the VIDEOS link, view the second group of videos (Compound Interest)

Study for Quiz 1 Friday, Ch 2-5; draw up 1 page of thumbnail sketches of essential functions covered in class, which you may use on the quiz.

Here is a scan of My essential function sketches

YOU MAY NOT USE MY PAGE. Copy it in your own hand.

**Fri-Sun** Do Ch 5 exercises #1-7 and continue if you need practice with the extra exponent practice.

View the last two Ch 5 videos at SUPPLEMENTAL MATERIALS, on continuous compounding and effective interest rate.

View all (yes, all) limit videos at VIDEOS

Read Ch 6. (Stay tuned here. One other post to come, which is practicing graphing piecewise functions.)

WEEK 3

**Mon** Did you watch all the limit videos? Watch them again and use them and the examples in the book to do as many of the problems as you can so far.

Do Exercises p. 67 #1-12, #16-30 even.

The short of it is this: To find a limit, first plug in the x = a given. If you don't get a number, but get 0/0 or number/0, then you have to resort to algebra. The videos are your friend. I will be, too, but not till Wednesday.

Hint: I have posted the solutions already, so you could follow along.

Read Ch 9 *Continuity*

**Wed** Today's lecture notes on Limits and Continuity

Continuity video 1 and Continuity video 2

Find several more, including videos on graphing piecewise functions under Continuity in VIDEOS

Do Ch 9 pp 84-85 #1 a-e, 2 a-d, 4, 5, 6

Read Ch 7 and Ch 8

Short quiz on Friday on, compound interest, limits and continuity. No notes are allowed on this quiz.

Ch 5 Know all the formulas, n = finite and continuous compounding. Know how to solve for t. Effective interest rate.

Ch 6 Know how to take limits of all types, given a function and/or a graph.

Ch 7 Know the criteria of 'f is continuous at a point x = a' to use when you justify whether a function is continuous or fails. Be able to Graph a piecewise function. The video has two clear examples.

Don't forget to check SUPPLEMENTAL MATERIALS and VIDEOS for extra helpful materials.

**Fri-Sun** Do Ch 7 Exercises p 72 #1, 2, 3 a-d

View Difference quotient (DQ) and the definition of derivative

related_rates_take-home_quiz.odt

WEEK 4

**Mon** Read Ch 8. Then, view the video, where Patrick finds the equation of the tangent line to f(x), but already has the derivative function f'(x) and evaluates it at the given point to get slope m. (Rather than doing the calculation of the limit of the DQ). This gives you the overall picture:
Finding equation of tangent line to the curve

Homework on limit of difference quotient to hand in on Wednesday! Remember, it's easier to find the general limit at x = a, then substitute the three values -1, 0, 1 into this (the derivative!)

Do Ch 8 Exercises p 78 #1, 2, 3, 4 *using the derivative formulas*

**Tues-Wed** *Review worksheets for Exam 1*

I've extracted and entitled Supplemental Materials worksheets here. Practice what you need:

- Equation of line tangent to f(x) worksheet #2a and #3 a,b only

Solutions are found at Solutions to worksheets

**Wed-Thurs** Exam 1 Topics:

Essential graphs; function of a domain (interval notation); piecewise functions; intercepts (y and roots); limits; continuity; linear cost, revenue, profit; compound interest (solving for various unknowns, whether F, P or t); slope of tangent using definition of derivative (limit of DQ etc.) and equation of tangent line at a point of f(x).

As usual, some interpretation of answers, like marginal cost, time to double with finite vs continuous compounding, word problems on derivatives.

I meant to post this: Compound interest summary

And here is what I did in class from Dan McKinney's practice: Practice for exam 1 and practice_for_exam_1_key.pdf

WEEKEND HW **Fri-Sun** Read Ch 10 (derivative rules) and view relevant videos:

WEEK 5

**Mon-Tues** Watch again Shortcuts to the derivative

Derivatives using power rule when n is not an integer

Do Ch 10, p 91 #3-6 and #16 a, b, c, d, o

I've moved some previous videos down, for Mon-Tues viewing:

View Basic product rule example

Proof of product rule using logs

Now do: Derivative worksheet Exercises 1 and 2 and Derivative worksheet for marginal cost, revenue, profit

Finally, view Chain rule explained

Read Ch 11

**Wed** Do Ch 10 p 91, #8-13 and #16 d-n

HELPFUL READING (*not* to hand in) The derivative and marginal cost, revenue and profit

View these short videos:

Ex of chain rule for radical function

Ex of chain rule for natural log function

Many great examples of chain rule involving ln[u(x)]

*Do* Ch 11 p 96 #1, and in each of the multi-part #2, 3, 4 EVERY OTHER DERIVATIVE

*Read* Ch 12 (easy chapter on Leibniz notation and higher derivatives)

QUIZ ON FRIDAY Ch 10 and Ch 11

Here are the derivative worksheets again, and their solution files:

Derivative extra practice and Solutions

Basic derivative worksheet (supplemental) and Solutions

Chain rule derivative worksheet (supplemental) and Solutions

**Fri-Sun** Do Ch 11 p 97 #6-9, and in the multi-part #13 EVERY OTHER DERIVATIVE

Do Ch 12 p 107 #1, 2, 4, 5, 7, 9

Check out the worked applications of Marginal cost, revenue, profit: Ex 1 and another example Ex 2, which motivate the take-home

To hand in Monday:

WORK INDEPENDENTLY OR NO CREDIT. More credit is gained for personal–even if faulty–work that has effort and time behind it than you get for copying a friend's, which gets no credit at all.

In the pdf, please ignore the note at the end, 'Compare to sketch we did in class on Wednesday'.

Feel free to use graphing program like Desmos to make your graph. It needs to be accurate, so you will want to scale your axes smartly.

WEEK 6

**Mon** Read Ch 13. View both Implicit Differentiation videos at
VIDEOS

Do Ch 13 exercises #1, 2, 3, 4, 8 (Tip: worked examples in the book will help you do homework problems)

**Wed-Thurs** First read related rates overview on Video page)

Then view:

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

Finally, read Ch 14 and another text chapter on ID and RR

Do Ch 14 pp 121-122 #1, 2, 4, 5, 6, 9, 12, 14 (again, videos and worked examples in text will help)

PRACTICE QUIZ Friday, to test how you handle derivative computation without formula sheet. Includes implicit differentiation. To mark at desks and keep to study for quiz that counts on Monday.

**Fri-Sun** Read Chapter 13.

At the VIDEOS view first video on critical numbers.

Related rates take home Please do this neatly so I may mark quickly and return it before exam.

WEEK 7

Exam 2 is this Friday.

Topics are Chapters 10-15.

**Mon-Wed** Do Exercises in Ch 15

View Extrema

Critical numbers of fcn and excellent example to illustrate

More about excellent example in previous video

Patrick mjt finds critical numbers of a fcn

Patrick mjt does a harder example

Do Ch 15 pp 129-130 #1, 2, 4 a-i

Supplemental worksheets:

Related rates worksheet and Related rates worksheet solutions

**Tues-Wed** Study these items for Exam 2, on Friday:

**Ch 10-11** Derivative (the 'u-forms', product, quotient, chain rules); study both word problems and computation of derivatives.

Marginal analysis: the meaning of marginal cost, revenue and profit

Graphs of parabolas and lines

Ch 10-11: Derivatives (the 'u-forms', product, quotient, chain rules); both word problems and computation

Here's some extra reading with worked examples on log and exponential derivatives

Marginal analysis: meaning of marginal cost, revenue and profit

Graphs of parabolas and lines

Ch 12: Leibniz notation, meaning of dy vs delta y (dy does not equal delta y unless the f is linear); higher order derivatives

Ch 13-14: Implicit differentiation and related rates: finding eqn of all tangent lines to curve at given x (be able to find y's); word problems in related rates, including geometric (circle, cylinder, triangle) and application to commerce: df/dt = (df/dx)(dx/dt) where f = C, R, P, and so on

Ch 15: Local extremes of a function and critical numbers: identify local extremes from sketch, know definition of critical numbers, find critical numbers c such that f'© = 0 and what c give DNE for f' (review domain so you know what to discard as a possible critical number), identify if, for critical number c whether f© is local max or local min by applying def of loc ext (that is, check f(x) for a NEARBY x < c and x > c)

WEEK 8

**Mon-Tues** View Ch 16 and Ch 17 videos:

Mean Value, Rolle's and Intermediate Value theorems

The lecturer presents the general IVT: f is cts on [a, b], f(a) < f(b), though the function doesn't change sign. I showed the particular case, where f(a) < f(b) because the function changes sign on the interval. It's a useful form of the IVT, since most applications concern zeros of function.

Increasing and decreasing functions

First derivative test for local extremes

Read Ch 17 only!

*Re-read Solutions Ch 15*

I posted Ch 17 solutions–to guide your Ch 17 exercises. Refer to videos above as well (first)

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

Do like the video and reading:

1. Find all critical numbers of f(x)

2. Put them on a number line

3. Inspect sign of f' in each interval created: does f increase (f' > 0), decrease (f' < 0), or do neither?

Check your work against the posted solutions. (This is a little flippy in terms of learning, but it's straightforward.)

**Wed** View Second derivative test for local extremes: concavity

In place of the quiz tomorrow, you will have a take home problem to work out and I will collect. Quiz upon your return.

Read Ch 18

**Fri** On the following video, pay close attention to a good technique (3:45 onward) for 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

And, my Summary of Ch 15, 17, 18 The alternate text and the videos are the best.

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

Here's my Example of a polynomial FDT and SDT for a polynomial

WEEK 9 HOMEWORK FOR THE WEEK OF SPRING BREAK

**Mon-Sun of Spring Break** You are responsible to read Chapters 19-21 over the break, covering the three classes of curves: polynomials, rational and root functions

View Limits at infinity (horizontal asymptotes--including "tricks" at 6:16)

Graphing a simple rational function

Graphing a harder rational function

Sketching a more involved rational fcn with FDT and SDT

Read Ch 19; Do exercises Ch 19 #1 a b c, #2 a b c d f i

Read Ch 20

WEEK 10

**Mon** Do exercises Ch 20 pp 167-168 #1 a b c, #3, 4 a-g #5 c d e f

Read Ch 21; do exercises p 174 #1, 2, 3

Read Ch 22, absolute extreme

people/mckenzie/math_220_hw.txt · Last modified: 2019/03/17 22:06 by mckenzie

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported