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All homework, in both text and WebAssign

Math 224/225 Syllabus

Math 224/225 Homepage

Links to the Daily Warm-up videos/slides in Math 224/225 Home Page linked in Daily HW below, as needed.

Here is the schedule of topics and test dates

DAILY HOMEWORK The boldface day indicates the day an assignment is given. The assumption is you will have attempted most of it and have questions for me in class.

Warm up videos and focus problems are also found in the links at the Math 224/225 Homepage

Log into WebAssign each day to see videos, do warm up exercises, and any graded homework by the due date. You'll also see prompts in Daily Homework below for this.

A note about WebAssign ​Generally, you will have 5 attempts on each WebAssign problem in the graded homeworks, with the exception of multiple choice, where you may have just one or two. For T/F, just the one!

On Skills Tests you do not get multiple attempts at each problem, but you can retake each test three times in the availability period.


Fri – I assigned the following:

1. Do 'Diagnostic Tests A, B and C' on pages xxvi-xxx (front of book). Check your answers and do the reviews which the book suggests, found in the book itself or on Stewart's website .

2. If you have not done so already, read 'Appendix A' (in the back of your book), and do the absolute value problems there (we did several on Wednesday).

3. Assigned in class–Read Chapter 1.5 (Intuitive limits) and 1.6 (Calculating limits).

Do 1.5 Exercises, pp 59-61: #1-9 odd, 11, 12, 17, 29, 30, 31, 33, 35, 40, 46

4. View the Limit videos “The Limit of a Function” and “Limit Laws” at Chapter 1 Warm Up Videos

Do Slides there, too.


Mon Re-read Chapter 1.6. Watch the Limit videos again.

Start 1.6 Exercises, p 70: #1-32 odd

Read Chapter 1.8 and view the videos for Chapter 1.8 “Continuity” at Chapter 1 Warm Up Videos

Do Slides, which are on the videos on the site.

Tues Log into WebAssign. If you have not done so already, please do the the first line “Getting Started” and the third line “Appendix A”. These are not graded, but they get you trained in the interface, and there is content in Appendix A, the absolute value, which we did the first day.

Wed Finish 1.6 Exercises, p 70: #1-32 odd

Read 1.4 and 2.1 and view corresponding videos in Chapter 1 Warm Up Videos and Chapter 2 Warm Up Videos

Your first graded assignment in WebAssign is due Sept 1.

Fri Start with these videos on limits:

Absolute value limit 1

Absolute value limit 2

Conjugate of radical limit

Examples using laws of limits

And finally, a good Summary video with many examples

Squeeze theorem

And finally, this one, which has several examples, but you can watch till you get the hang of it:

Limits of trig fcns using limit of (sin x)/x

Re-read 2.1. View “Tangents, Derivatives, and Rates of Change” in Chapter 2 Warm Up Videos


Mon No Class Labor Day. Drop Deadline is Wednesday, Sept 4. Keep working on 1.4 and 2.1.

Tues 8-O Read Ch 2.2 Derivative as a Function & Differentiation Formulas

Watch first three Ch 2 Warm Up Videos AGAIN! “Differentiation Formulas”, “Trig Derivatives”, “Chain Rule”

Stay on top of WebAssign!

Begin App D, Diagnostic test on Trig Functions

Wed We'll review all the big ideas so far, and get deep into derivative rules so we can compute derivatives.

Do the Warm-Up on WebAssign for Skills Test 1

QUIZ FRIDAY: A few limits, continuity, domain of functions, solve absolute value equation and/or inequality, slope of tangent as derivative of function (meaning limit of difference quotient). Short!

Fri Catch up on reading Ch 2.3 and 2.4 (differentiation formulas, algebraic through trigonometric functions)

Please watch the rest of the Ch 2 videos up to Chain Rule , and look at the slides.

8-O You might want to print the slides so you can write on them and fix your errors when we go over them in class.


Mon Read Ch 2.5. Do Warm ups and slides and have questions for me tomorrow on past slides and any trig questions, including precalc type questions.

You should have done the App D Trig Diagnostic Test in Stewart. Now check against the Complete Solutions to Diagnostic Tests

8-O EXAM 1 is on SEPT 16 8-O It covers through Ch 2.5 Chain Rule, which is our last topic, to be covered Wed.

Archived quizzes for practice These are not comprehensive of the exam, but a good barometer of your ability to sit for the formal in-class exam.

Please do independently without notes (till you get truly stuck) and bring in for review day on Friday. I will add an archived trig and chain rule quiz tomorrow.

Archived quiz 1

Archived quiz 2a

Archived quiz 2b

Wed Chain rule is the lecture, as well as trig derivative slides.

Finish the archived quizzes and any warm ups on the schedule. Be ready with questions on Friday Review. After doing the chain rule slides, we will go over archived quizzes and older slides.

8-) Mini-quiz on Friday on using limit of DQ definition for f'(x) to find a derivative of a given f(x); question on piecewise function and discontinuity/continuity; find eqn of line tangent to a graph at a given point.

Fri Do the in-class that became a Take-home quiz. Hand in Monday (NO LATES ACCEPTED).

Big ideas, Exam 1

“From the Math 224/225 course website, here are several exams from previous semesters, to give you a sense of what types of problems have been asked in semesters past. Exams this semester may not bear much similarity to these:”

Solutions to 224 Exam 1, Sept 19, 2016

Solutions to 224 Exam 1, Spring 2016

Solutions to 224 Exam 1, Fall 2015


At Stewart e-book, where the answers for some appear when you click on the box under the question.

Appendix A #1-12 odd, 43-45

Ch 1.6 #1, 2, 11-31 (odd is ok), #41-46 ALL (important limits of abs value fcns)

Ch 1.8 #1-8 and 15-22, 39, 40

Ch 2.1 #10-15, 17-35 odd, 47-55 odd

Ch 2.2 #3, 19-29 odd, esp for domain (you can do the derivative using the appropriate rule rather than definition), #30 is important function to graph, though we aren't sketching yet it's a transformation of sq rt x, #39-42 ALL, 49, #57, 62

Ch 2.3, 2.4 and 2.5 are the derivative rules (power, prod, quot, trig, chain). Choose as many as you feel you still need from the computation exercises for extra practice


Mon Recovered from Exam 1? Read Ch 2.6 and 2.7 and watch the relevant Chapter 2 Warm Up Videos 'Implicit Differentiation' and 'Rates of Change in Sciences'

Stay current on WebAssign



1. Review Ch 2.7 implicit differentiation (ID) for short quiz Monday

2. Finish Ch 2.8 related rates (RR) reading

3. Here are some videos I use in Math 220:

ID and RR

RR 1: Area of circle and changing radius rate

RR 2: Area of triangle and changing side length rate

RR 3: Ladder sliding down the wall problem

Cost and profit with respect to time

van der Waals equation, which is more precise than the ideal gas law because small changes in V and P are not ignored (something that is allowable for gases at std temp and pressure)

4. 8-) Related Rates Worksheet and the Solutions to Related Rates Worksheet

5. m( SLIDES: With some exclusions and some assistance: ID Slides decent, but somewhat challenging. [I will post solutions soon.]

RR in Science Slides come with this note from Dr Kaz:

Slide 1(a), dV/dx should read dV/dt ; Slide 5, ignore; Slides 8-11, ignore


Mon Finish related rates HW on WebAssign and understand the slides covered

Read 3.1 and view 3.1 'Critical Numbers' Warm up videos and slides

Finish the In-class Quiz 3 and Take home portion REVISED

Staple completed work together and hand in Wednesday.

Wed Whenever I forget to post HW, as I did last night, you can find the reading and warm-up videos at Schedule of topics and test dates

That said, Read 3.3; view 3.3 'The Shape of the Graph' Warm up videos and slides

Stay current on WebAssign

Pop quiz tomorrow on Parent function sketches (translations possible)


Fri-Mon Rosh Hashana

Read 3.4 and view 3.4 'Limits at Infinity' and 3.5 'Curve Sketching' Warm-up videos

Stay current on WebAssign

Wed Read 3.5 and continue with the videos and review the slides. I will post more Thursday.

Thurs Study the Curve-sketching summary

Can you think of a super simple function that illustrates why, if f''(c) = 0, then c is not necessarily an inflection point of f(x). You'll find it in the “Curve-sketching summary”.

8-O There's an exercise at the end of “Calculus of Curve Sketching”, due Oct 14.

Fri Continue Thursday's, inc Dr Kaz's take home, due Oct 11.


Mon Read Ch 3.5 and choose textbook and/or slide problems to ask in class, except the take home ones.

Reminder:You can take 2nd or 3rd attempt any weekday thru to last day of class. You'll find this info in the weekly schedule of topics, too.

Here's Dr Kaz's Curve sketching assignment

Wed No class (Yom Kippur). Catch up on curve sketching, and don't forget to have questions for me for Friday.

8-) I moved the due date of my curve sketching question at the end of the Summary handout to Oct 14.

Dr Kaz's is still due Oct 11.

Stay current on WebAssign !

The in-class final is Monday. We'll review on Friday, starting with doing a few graphs.

Fri The Math 224 final is Monday.

Topics to study: Basically, anything learned in Ch 1, 2, 3 as covered in HW, but especially related rates and curve sketching, implicit differentiation, derivative concepts.

Here are some other useful videos:

End behavior, rational functions

End behavior, exponential and polynomial

Curve sketching summary


Monday was the final for Math 224. Wednesday was off. Here begins Math 225

Fri Read Sec 3.7 in the text, view the Warm up Video on Optimization and do the Ch 3.7 Warm Up question 2 in WebAssign (we did the question 1 in class)

Work on Ch 3.7 slides for Monday

View Patrick mjt on Optimization


Mon Do the Optimization take-home due Friday.

Read Sec 3.9 and view the Ch 3.9 Warm-up video

Ch 3.9 WebAssign Warm Up is due Oct 23.

Wed There weren't any videos I could find on WA for solving for the constant of integration given boundary (or initial) conditions, so please view Solving for C given initial conditions

Then, work on Slides for 3.9 for HW to share in class Friday.

Read Ch 4.1 and view Warm up videos.

Fri Stay current on Practice items on WebAssign. There's a quiz on Monday on antiderivatives (not Reiemann sum, but definitely on the main antiderivatives and initial condition problem to solve for constant of integration).

The slides will help; on Saturday I'll post exercises in Ch 3.9 to study, as well as Ch 4.1.


Mon Read 4.2 and 3.2. Do the warm ups on time

View 4.2 and 3.2 warm up videos

Write down the properties of the definite integral and look back to this page for associated problems I'll assign for each.

Any questions about 3.9 and 4.1? Ask in class Wednesday!! Otherwise, all 4.2 and 3.2 that day.

NEW: Do Ch 4.1 #21, 22, 23 in the e-book (not connected to the Gauss and Archimedes, except to help you understand sigma notation)

Here's a Perfectly clear video on the proof of the MVT


Wed Read Ch 4.3. More to come

Fri Continue reading and viewing related material on Ch 4.3, FTC 1 and 2

Do textbook problems on MVT in Ch 3.2: #9-17 odd, and FTC in Ch 4.3: #7-17 and #21-37 odd.

Short quiz on MVT and FTC tomorrow (end of class)!


Mon-Wed Sorry I didn't fill in this line, but you did reading of Ch 4.4 and the videos and slides there. Also, stay current on WebAssign and choose questions for me to review on Friday to review for the Monday exam.


8-o Focus on problems previous tests and solutions posted by director and on my suggestions at the end of the sections shown:

Ch 3.2 #7-21 odd; Ch 3.7 #21-29 odd; Ch 3.9 #27-37 odd, #53-63 odd; Ch 4.1 #7, 8, 21, 23; Ch 4.2 #17-29 odd; Ch 4.3 #7-41 odd, #49-55 ALL; Ch 4.4 #5-15 odd and #19-39 odd

Solution to #56 esp from Stewart (alternate to way textbook and I do it). I can't seem to get it right side up, so you will have to do that:


Mon Ch 4.5 read text and do WebAssign warm up and videos for this section.

Wed Continue doing u-substitution, challenge yourself with the slides. We will have a mini-quiz on Friday : P

Fri to Sun Quiz on u substitution and FTC

Read Ch 5.1 and view Ch 5.1 videos

Do the warm-up in WebAssign

If you can, print the slides and bring them to class


Mon Ch 5.2 and view Ch 5.2 videos. Do warm up in WebAssign

m( Looking back: Each week till the end of the semester, I will post 'looking back' videos and problems concerning insights of the previous topics that were perhaps a little slippery. Graph interpretation, true/false motivated by the main theorems, that sort of thing. Here is the first: Interpreting a graph of f'(x) for concavity

Identify problems on the slides you would like us to work out in class

people/mckenzie/math224.txt · Last modified: 2019/11/18 21:27 by mckenzie