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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

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

REVISED **Tues/Wed/Thurs**

*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.

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)

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

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

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

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:

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** 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 #1-6, #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** 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** Review these focus topics for the exam:

people/mckenzie/math_220_hw.txt · Last modified: 2018/09/19 11:44 by mckenzie

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