## MATH 16A (SECTION 001) , 198 Young , 8-8:50 am MWF ## Instructor: Dr. D. A. Kouba

Last Updated: December 11, 2020

Text: CALCULUS, An Applied Approach (7th edition) by Larson and Edwards

Office: 3135 MSB (Mathematical Sciences Building)

Phone: (530) 754-0469

My Office Hours: Via Zoom

## Mathematics Placement Requirement (MPR) All students enrolling in Math 16A are required to satisfy the MPR. The MPR can only be satisfied by Passing the Math Placement Exam with an overall score of at least 30 AND a trig score of at least 2. Find further information HERE .

The following quizzes were given during Summer Session 2007, Summer Session 2008, and Summer Session 2010. You can use them as a source of optional supplemental practice problems.

Quizzes given during Summer Session 2007.

Quiz 1 , KEY ..... Quiz 2 , KEY ..... Quiz 3 , KEY ..... Quiz 4 , KEY ..... Quiz 5 , KEY ..... Quiz 6 , KEY ..... Quiz 7 , KEY ..... Quiz 8 , KEY ..... Quiz 9 , KEY

Quizzes given during Summer Session 2008.

Quiz 1 , KEY ..... Quiz 2 , KEY ..... Quiz 3 , KEY ..... Quiz 4 , KEY ..... Quiz 5 , KEY ..... Quiz 6 , KEY

Quizzes for Summer Session 2010.

Quiz 1 , KEY ..... Quiz 2 , KEY ..... Quiz 3 , KEY ..... Quiz 4 , KEY ..... Quiz 5 , KEY ..... Quiz 6 , KEY .....

The course will likely cover the following sections in our textbook : 1.1-1.6, 2.1-2.8, 3.1-3.4, 3.6-3.8, 8.1-8.4

**** Here are Basic Math Formulas .

**** Here are Algebra Review Problems.

**** Here are Trigonometry Graphs, Values, and Identities .

**** Here are copies of Worksheets , Supplemental Algebra Problems , and Supplemental Trigonometry Problems .

**** Here are Supplementary Class Handouts .

___________________________________________________________________________________________________________

++++++++ ..... Here are Practice Exam 1 and Solutions .

++++++++ ..... Here are Practice Exam 2 and Solutions .

++++++++ ..... Here are Practice Exam 3 and Solutions .

++++++++ ..... Here are Practice Final Exam and Solutions .

___________________________________________________________________________________________________________

### Click here for additional optional PRACTICE PROBLEMS with SOLUTIONS found at THE CALCULUS PAGE , a website which I created.

Here are some TIPS for doing well on my exams.

## HERE ARE HOMEWORK ASSIGNMENTS, LECTURE NOTES, AND SHORT VIDEOS

SCANNED PROBLEMS for Sections 1.1-1.6, 3.6, and 8.1-8.3

-- Here are detailed class notes covering topics from Pre-Calculus Review (Topics: Pythagorean Theorem, Distance Formula, Midpoint Formula, Circles, Sign Charts, and Polynomial Division)
-- Here is a video using Completing the Square in order to find the center of a circle.
-- Here is a video showing how to use Sign Charts to solve inqualities.
-- Here is a video showing how to rewrite rational expressions using Polynomial Division.

• HW #1 ... (Section 1.1) ... p. 8: 3, 4, 10, 13-16, 19, 23, 26, 28, 31, 32, 35, 36, 41, 43a ... and ... (Section 1.2) p. 21: 3, 5, 7-13, 15, 18, 20, 23, 29, 31, 32, 35, 38, 41, 44, 46, 48, 53, 55, 59, 60, 62, 63, 66

-- Here are detailed class notes covering additional topics from Pre-Calculus Review (Topics: Slope, Lines (Parallel and Perpendicular), Similar Triangles, Functions, One-to-One, Composition, Inverses, and Domain and Range)
-- Here is a video showing Examples of Functional Composition .
-- Here is a video where the Domain and Range of Functions are determined .
-- Here is a video where a function is shown to be One-To-One using the algebraic definition. Then it's Inverse Function is found.

• HW #2 ... Here are notes on Functions and Inverses of functions ... Here is an example of Functional Composition from physics ... (Section 1.3) ... p. 33: 2, 5, 6, 8, 14, 15, 21, 27, 31, 34, 38, 44, 47, 50, 51, 64, 67, 69, 81, 82, 83, 86, 88 ... and ... (Section 1.4) p. 45: 2, 5, 8, 12, 17, 18, 19, 22, 23, 26, 27, 30, 31, 32, 36, 38, 39, 42, 47, 54, 55, 60, 62, 63, 70, 72, 75 ... and ... Worksheet 1 : 1-10 ... and ... SuppAlg : SA1, SA3

-- Here are detailed class notes covering Limits of Functions (Topics: Indeterminate Forms, One-Sided Limits, and Infinite Limits)
-- Here is a video showing Examples of algebraic computation of Limits .
-- Here is a video showing Examples of graphical computation of Limits. This includes One-Sided Limits and Limits to + or - Infinity.

• HW #3 ... (Section 1.5) ... p. 58: 2, 6, 9-12, 17, 19, 22, 23, 29, 32, 37, 40, 42, 44, 47, 50-52, 56, 57, 59-62, 64, 68 ... and ... Worksheet 1 : 11, 12, 14-16, 19, 23 ... and ... SuppAlg : SA2, SA5

-- Here are detailed class notes covering Limits to + or - Infinity (Topics: Indeterminate Forms, Vertical Asymptotes, Horizontal Asymptotes, and Tilted Asymptotes)
-- Here is a video showing Limits to + or - Infinity .
-- Here is a video (TYPO: "x+1" should be "x+3".) showing how to find Horizontal Asymptotes .
-- Here is a video showing how to find Vertical Asymptotes.
-- Here is a video showing how to find Tilted Asymptotes.

• HW #4 ... (Section 3.6) ... Here are notes and optional practice problems for Horizontal, Vertical, and Tilted Asymptotes ... p. 228: 1, 3, 4, 6, 9-16, 19, 22-24, 26-29, 31, 32, 37, (On the following six problems use x- and y-intercepts and vertical and horizontal asymptotes to sketch each graph. Do NOT use extrema or inflection points) 41, 43, 48, 52, 54, 56, 59, 63, 64 ... and ... Worksheet 1 : 13, 17, 18, 20, 26

-- Here are detailed class notes covering Continuity of Functions. There are three categories of Continuity Problems-- Continuity of y=f(x) at x=a (The Three-Step Process), Continuity and Shortcuts, and Continuity and "Fake Graphs".
-- Here is a video of Examples showing how to determine Continuity of a Function y=f(x) at x=a (Three-Step Process).
-- Here is a video of Examples showing how to determine Continuity of a Function y=f(x) using Shortcuts .
-- Here is a video of Examples showing Continuity and "Fake Graphs."

• HW #5 ... (Section 1.6) ... Here are notes on the Continuity of a function ... p. 69: 3, 5, 11, 14, 21, 25, 27, 30, 39, 44-46, 60 ... and ... Worksheet 2 : 1(Use a FAKE GRAPH and LIMITS.), 2 ... and ... Worksheet 1 : 21, 22, 24, 25, 27-29

-- Here are detailed class notes covering Trig Review. Included in these notes are Trig Identities and Trig Values of common angles.
-- Here is a (CORRECTION: " f '(theta)=0 " on whiteboard should be " the following trig equations ".) video showing Examples where we solve trig equations.

• HW #6 ... (Section 8.1) ... Here are Trig Review Sheets ... p. 555: 9, 10, 13-16, 21-24, 28, 30-34, 36, 37, 40, 41, 47, 48, 50, 53, 54 ... and ... (Section 8.2) ... p. 566: 1, 5, 8, 10, 12, 26, 28-30, 47, 50-52, 55, 63, 65 ... and ... (Section 8.3) ... p. 575: 9, 14, 16, 28, 32, 40, 59, 62 ... and ... Worksheet 3 : 1-4 ... and ... SuppTrig :ST1 Bring It On !

EXAM 1 is Friday, October 16, 2020. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 6, and material from sections 1.1-1.6, 3.6, and 8.1-8.3 in the book which was presented in lecture notes through the trigonometry material Wednesday, October 14, 2020.

TYPES OF QUESTIONS FOR EXAM 1 FOR FALL 2020 (subject to change)

• 4 -- limits
• 2 -- domain/range
• 1 -- continuity (using the three-step process at x=a, discussing general continuity using shortcuts, or solving for unknown constants using limits and a fake graph)
• 1 -- trigonometry
• 1 or 2 -- functional composition/one-to-one function/inverse function
• 1 -- asymptote
• 1 -- circle
• 2 or 3 -- others

HERE ARE SOME RULES FOR EXAM 1.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. THANK YOU FOR YOUR COOPERATION.
• 2.) YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You may NOT use L'Hopital's Rule to compute limits on this exam.
• 4.) You may NOT use shortcuts from the textbook for finding limits to infinity.
• 5.) You need NOT MEMORIZE trigonometry identities.
• 6.) Using only a calculator to determine the value of limits will receive little credit.
• 7.) You will be graded on proper use of limit notation.
• 8.) Put units on answers where units are appropriate.
• 9.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
Most of the exam questions will be homework-type, practice exam-type questions.

THE GRADING SCALE FOR EXAM 1 FOR FALL 2020 IS :

A ...... 112-125

A-/B+ ...... 108-111

B ...... 87-107

C ...... 65-86

D ...... 50-64

F ...... 0-49

SCANNED PROBLEMS for Sections 2.1-2.4 and 8.4

-- Here are detailed class notes covering The Derivative of a Function y=f(x). We first view the Derivative as defined by a Limit. Then we determine that the Derivative also represents the SLOPE of a Tangent Line to the graph of y=f(x).
-- Here is a video where Derivatives of Functions are determined using the Limit Definition.

• HW #7 ... (Section 2.1) ... p. 90: 5-12, 14, (Use the limit definition of derivative on the next seven problems) 15, 18, 22, 25, 32, 34, 43, 49, 50, 51 (Use the limit definition of derivative to "prove" that y=x^{2/5} is not differentiable at x=0.), 52-54

-- Here are detailed class notes covering The Derivative of a Function. Here we include Units and view the Derivative as the SLOPE of a Tangent Line as well as a Rate of Change.
-- Here are brief notes explaining when a Derivative does Not Exist at a point x=a. This would be where the graph at x=a is a "corner", a point of discontinuity, or has a Vertical Tangent Line.
-- Here is a video of two Examples where we Sketch the Graph of the Derivative f' using the Graph of the Function f.
-- Here is another video of two more Examples where we Sketch the Graph of the Derivative f' using the Graph of the Function f. These Examples use graphs with points where the Derivative Does Not Exist !
-- Here is another video (CORRECTION: "m=2.5" should be "m=-2.5", st that f' should be below the x-axis at y=-2.5.) of one Example where we Sketch the Graph of the Derivative f' using the Graph of the Function f. This Example uses a graph with points where the Derivative Does Not Exist !

• HW #8 ... (Section 2.1) ... I.) Find all points (x, y) on the graph of y = 4x-x^2 with tangent lines passing through the point (2, 5). You may assume that the derivative of y = 4x-x^2 is y'=4-2x. ... and ... Worksheet 4 : 1, 2 ... and ... SuppAlg : (For the following problem you will need information found HERE .) SA4, SA7, SA9, SA10, SA11

-- Here are detailed class notes covering Rules for Differentiation (Shortcuts).
-- Here is a video of Examples using the Rules for Differentiation (Shortcuts).
-- Here are Examples of "Careful Reading Problems" .

• HW #9 ... (Section 2.2) ... Here is a proof that the derivative of line f(x)=mx+b is f'(x)=m ... p. 102: 1, 4-20, 23, 26, 30, 31, 33-36, 40, 44, 45, 48, 49, 51, 53, 61, 65, 66 ... and ... SuppAlg : SA8, SA15

-- Here are detailed class notes covering Average Rate of Change and Instantaneous Rate of Change for a Function y=f(x).
-- Here is a video of a "practical" Example of Average Rate of Change (ARC) and Instantaneous Rate of Change (IRC).

• HW #10 ... (Section 2.3) ... Here is an example using ARC (Average Rate of Change) and IRC (Instantaneous Rate of Change) ... p. 116: 1, 3, 6, 8, 12, 14-16, 32, 33cde, 43 ... and ... SuppAlg : SA6, SA12

-- Here are detailed class notes covering the Product Rule, Triple Product Rule, and Quotient Rule . Here is a Proof of the Product Rule Using the Limit Definition of Derivative. Here is a Proof of the Quotient Rule Using the Limit Definition of Derivative.
-- Here is a video of Examples using the Product Rule and the Triple Product Rule.
-- Here is a video of Examples using the Quotient Rule.

• HW #11 ... (Section 2.4) ... Here are Derivative Rules for the Product Rule, the Triple Product Rule, and the Quotient Rule ... Here is a Proof of the Product Rule and a Proof of the Quotient Rule ... p. 128: 1, 3, 6, 8, 12, 25, 30, 32, 33, 37, 38, 45-48, 55, 57 ... and ... SuppAlg : SA17

-- Here are detailed class notes covering Trig Derivatives .
-- Here is a video of Examples using Trig Derivatives.

• HW #12 ... (Section 8.4) ... Here are Derivative Rules for Trig Functions ... Here is a Proof for the Derivative of sin x ... p. 585: 1-12, 39, 40, 43, 44 ... and ... SuppAlg : SA16
EXAM 2 is Friday, November 6, 2020. It will cover handouts, lecture notes, and examples from class, homework assignments 7 through 12, and material from sections 2.1-2.4 and 8.4 in the book which was presented in lecture notes through the material on derivatives of trigonometry functions on Wenesday, October 28, 2020. You are expected to memorize all the shortcut rules for differentiation presented in class. We can do this !

MEMORIZE the following list of derivative rules.

1. D(c) = 0
2. D(mx+b) = m
3. D(f(x) +/- g(x)) = f'(x) +/- g'(x)
4. D(c f(x)) = c f'(x)
5. D(x^n) = n x^(n-1)
6. (Product Rule) ... D(f(x)g(x)) = f(x)g'(x) + f'(x)g(x)
7. (Triple Product Rule) ... D(f(x)g(x)h(x)) = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)
8. (Quotient Rule) ... D(f(x)/g(x)) = {g(x)f'(x) - f(x)g'(x)}/[g(x)]^2
9. D(sin x) = cos x
10. D(cos x) = - sin x
11. D(tan x) = sec^2 x
12. D(sec x) = sec x tan x
13. D(cot x) = - csc^2 x
14. D(csc x) = - csc x cot x

TYPES OF QUESTIONS FOR EXAM 2 FOR FALL 2020 (subject to change)

• 1 -- limit definition of a derivative
• 1 -- sketch f' from graph of f
• 4 -- various derivatives using above rules (NO SIMPLIFICATION OF ANSWERS, NO CHAIN RULE)
• 2 -- solve f'(x)=0 for x and set up a sign chart for f'
• 1 -- average and instantaneous rate of change using a graph like we did in class
• 1 or 2 -- find equation of tangent or perpendicular line
• 2 or 3 -- others

HERE ARE SOME RULES FOR EXAM 2.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You may NOT use L'Hopital's Rule to compute limits on this exam.
• 4.) You may NOT use shortcuts from the textbook for finding limits to infinity.
• 5.) You may NOT use the Chain Rule on this exam.
• 6.) You will be graded on proper use of limit notation.
• 7.) Put units on answers where units are appropriate.
• 8.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
Most of the exam questions will be homework-type, practice exam-type questions.

THE GRADING SCALE FOR EXAM 2 FOR FALL 2020 IS :

A ...... 112-125

B ...... 81-111

C ...... 60-80

D ...... 45-59

F ...... 0-44

SCANNED PROBLEMS for Sections 2.5-2.8, 3.1-3.3, 3.7, and 8.4

-- Here are detailed class notes covering the ChainRule .
-- Here is a video of Examples using the Chain Rule.

• HW # 13 ... (Section 8.4 and 2.5) ... p. 585: (Do not simplify answers. Do not use trig identities. Omit problems 13, 14, 22, 25, 26, 31. These will be covered later in Math 16B.) 15-21, 23, 24, 28, 36, 41, 46 ... and ... p. 138: 17, 22, 23, 30, 38, 39, 49, 59, 64, 67, 70, 73, 74 ... and ... Worksheet 5 ... and ... SuppTrig : 6

-- Here are detailed class notes covering Higher-Order Derivatives .
-- Here are detailed class notes covering Gravity Problems .
-- Here is a video of Examples using Higher-Order Derivatives.
-- Here is a video of Examples using Gravity Problems.

• HW # 14 ... (Section 2.6) ... p. 145: 1, 4, 7, 11, 13, 16, 19, 20, 21, 24 (On next four problems solve f'(x) = 0 and f''(x) = 0 for x.) 34, 35, 38, 40, 41-43, 50abcde ... and ... Gravity Problems and Solutions ... Here are links to applications in physics of the third derivative, called jerk , and the fourth derivative, called snap (jounce) .

-- Here are detailed class notes covering Relative and Absolute Extrema (Max's and Min's) .
-- The following videos show how to use a first derivative sign chart to find Relative and Absolute Maximums and Minimums ... video 1 ... video 2 ... video 3

• HW #15 ... (Section 3.1) ... (Set up a sign chart for y'. Clearly label critical points and y-values and identify relative maximums and minimums.) p. 179: 2, 3, 6, 8, 14, 15, 18, 22, 23, 25, 27, 35a, 40a ... and ...(Section 3.2) ... (Set up a sign chart for y'. Clearly label critical points and y-values and identify relative and absolute maximums and minimums. Sketch the graph.) p. 189: 5, 8, 16 (Also check for vertical asymptote.), 18 (Also check for horizontal asymptote.), 20, 21 (Use interval[-1, 2].), 23 (Use interval [-1, 4].), 44 (Change $100 to$25.), 45

• Here are DETAILED GRAPHING INSTRUCTIONS :
1. State the DOMAIN of the function.
2. Take the FIRST derivative and set up a SIGN CHART for f'(x). Clearly mark the solutions to f'(x)=0 and their y-values, and identify all RELATIVE and ABSOLUTE maximum and minimum values.
3. State the OPEN INTERVALS on which f is INCREASING and DECREASING.
4. Take the SECOND derivative and set up a SIGN CHART for f''(x). Clearly mark the solutions to f''(x)=0 and their y-values, and identify all INFLECTION POINTS.
5. State the OPEN INTERVALS on which f is CONCAVE UP and CONCAVE DOWN.
6. Determine all X-INTERCEPTS and Y-INTERCEPTS.
7. If appropriate, determine all HORIZONTAL ASYMPTOTES (H.A.).
8. If appropriate, determine all VERTICAL ASYMPTOTES (V.A.).
9. DRAW a rough SKETCH of the graph of y=f(x) and CLEARLY identify the coordinates of all important points on the graph.

-- Here are detailed class notes covering Detailed Graphing .

• HW #16 ... (Section 3.3) ... Here are Instructions for Detailed Graphing Problems and here are some Notes and Examples ... Here is a biological example of an Inflection Point ... p. 198: 1, 6, 7, (Do DETAILED GRAPHING for the next 8 problems.) 15, 27, 29, 35, 39, 44-46, 65ab

• HW #17 ... (Section 3.7) ... p. 238: (Do DETAILED GRAPHING for all problems.) 1, 2, 9, 17, 22, 23, 24, 34, 35, 40 ... and ... (Section 3.2) ... p. 189: (Do DETAILED GRAPHING for all problems.) 22, 23 ... and ... (Do DETAILED GRAPHING for all problems except SuppTrig: ST2.) I. f(x)=sinx+cosx on interval[0, pi], II. f(x)=-\sqrt{3}cosx-sinx on interval [0, 2pi] ... and .. SuppTrig : ST2, ST3ab.

• ... Can we use the FIRST derivative to determine INFLECTION points ? ... The answer is surprisingly "sometimes YES " !!! ...

-- Here are detailed class notes covering Implicit Differentiation .
-- Here is a video of Examples using Implicit Differentiation.
-- Here is a video of an Example using Implicit Differentiation to sketch the portion of a graph.

• HW #18 ... (Section 2.7) ... p. 152: 1, 4, 6, 10, 15, 18, 22, 24, 30, 34, 36, 40, 45 ... and ... (Section 8.4) ... p. 586: 47, 48

-- Here are detailed class notes and examples covering Related Rates Problems.
-- Here is a video of one Example of a Related Rates Problem.
-- Here is a another video of one Example of a Related Rates Problem.

• HW #19 ... (Section 2.8) .... Here is a Strategy for solving Related Rates Problems and their Solutions , many of which will be covered in class ... p. 160: 2, 5, 6, 9, 10, 13, 17ac ... and ... Worksheet 6 ... and SuppTrig : ST4, ST5

• HW #20 ... (Section 2.8) ... p. 160: 16, 18-20, 23 ... and ... (Chapter 2 Review) p. 169: 99 ... and ... Worksheet 7
EXAM 3 is Friday, December 4, 2020. It will cover handouts, lecture notes, and examples from class, homework assignments 13 through 20, and material from sections 2.5-2.8, 3.1-3.3, 3.7, and 8.4 which was presented in lecture notes through Monday, November 23, 2020. You are expected to know the 14 rules of differentiation, which were needed on Exam 2.

TYPES OF QUESTIONS FOR EXAM 3 FOR Fall 2020 (subject to change)

• 2 or 3 -- chain rule
• 1 -- gravity problem (MEMORIZE GRAVITY EQUATION: s(t)= -16t^2 + (v_o)t + (s_o) )
• 2 -- implicit differentiation
• 2 -- related rates
• 1 -- complete detailed graphing (NOTE: I will provide you with the function f(x) and its derivatives f'(x) and f''(x) !)
• 2 -- partial detailed graphing (finding just max/min or just inflection points, etc.)
• 1 or 2 -- Others

HERE ARE SOME RULES FOR EXAM 3.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You will be graded on proper use of derivative notation.
• 4.) Put units on answers where units are appropriate.
• 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

Most of the exam questions will be homework-type, practice exam-type questions.

THE GRADING SCALE FOR EXAM 3 FOR FALL 2020 IS :

A ...... 112-125

B ...... 78-111

C ...... 55-77

D ...... 41-54

F ...... 0-40

SCANNED PROBLEMS for Sections 3.4, 3.5, and 3.8

-- Here are detailed class notes and examples covering Maximum/Minimum Optimization Problems.
-- Here is a video of one Example of a Maximum/Minimum Optimization Problem.
-- Here is another video of one Example of a Maximum/Minimum Optimization Problem.
• HW # 21 ... (Section 3.4) ... Here are examples of Maximum/Minimum Optimization Problems which will be covered in class ... p. 207: 1, 4, 6-9, 11, 13, 18, 20, 22 ... and ... MaxMinHW: I

• HW # 22 ... Here is an Example from Economics about Maximizing Profit and its Solution ... (Section 3.4) ... p. 207: 14, 24, 25c, 26, 28, 35, 39 ... and ... MaxMinHW: II, III

• HW # 23 ... (Section 3.5) ... p. 219: 19, 20, 23, 25 ... and ... MaxMinHW: IV, V, VI, VII, VIII

-- Here are detailed class notes covering The Differential of a function y=f(x).
-- Here are Examples where we use a Differential to Estimate the Value of Numbers . And here is a video with such Examples.
-- Here are Examples where we use a Differential to Estimate Propagated Percentage Errors . And here is a video with one such Example.

• HW #24 ... (Section 3.8) ... and p. 246: 11, 12, 17, 37-39, 40-42 ... and ... Worksheet 8 : You can get there !

The FINAL EXAM is Friday, December 18, 2020, 7:45-10:15 am.

BRING A PICTURE ID TO THE EXAM
AND BE PREPARED TO SHOW IT TO KOUBA OR THE TEACHING ASSISTANTS !!

The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 24, and material from sections 1.1-1.6, 2.1-2.8, 3.1-3.4, 3.6-3.8, 8.1-8.4. You are expected to know the 15 rules of differentiation, which were needed on Exam 2. Use your three hour exams, 24 homework assignments, and the practice exams as a guide to your preparing for the final exam.

TYPES OF QUESTIONS FOR THE FINAL EXAM FOR FALL 2020 (subject to change)

• 3 -- limits
• 3 -- max./min optimization
• 1 -- related rates
• 2 -- differentials
• 1 -- limit definition of derivative
• 1 -- complete detailed graphing
• 2 -- solve f'(x)=0 or f''(x)=0 for x
• 1 -- velocity/acceleration (gravity problem)
• 1 -- implicit differentiation
• 1 -- find equation of tangent line or perpendicular line
• 1 -- Other

HERE ARE SOME RULES FOR THE FINAL EXAM.

• 0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 2.) You may NOT use L'Hopital's Rule to compute limits on this exam.
• 3.) You may NOT use shortcuts from the textbook for finding limits to infinity.
• 4.) You need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
• 5.) Using only a calculator to determine the value of limits will receive little or no credit.
• 6.) You will be graded on proper use of limit notation.
• 7.) Put units on answers where units are appropriate.
• 8.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

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