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.
Wed to Thurs: Read Ch 1 and 2; view first five videos at SUPPLEMENTAL MATERIALS
Do p 5 exercises: #1, 2, 7, 8
Do p 16 exercises: #9-15
Fri-Sun View Graphing piecewise functions; do rest of Ch 2 exercises, pp 15-16, #1-6
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
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)
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.)
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
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.
Fri-Sun Do Ch 7 Exercises p 72 #1, 2, 3 a-d
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:
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
WEEKEND HW Fri-Sun Read Ch 10 (derivative rules) and view relevant videos:
Mon-Tues Watch again Shortcuts to the derivative
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:
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:
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:
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
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.
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)
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.
Exam 2 is this Friday.
Topics are Chapters 10-15.
Mon-Wed Do Exercises in Ch 15
Do Ch 15 pp 129-130 #1, 2, 4 a-i
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)
Mon-Tues View Ch 16 and Ch 17 videos:
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.
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.)
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!
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
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
Read Ch 19; Do exercises Ch 19 #1 a b c, #2 a b c d f i
Read Ch 20
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