• EXAM 1-- Wednesday, October 18, 2017
  
  
• EXAM 2-- Wednesday, November 8, 2017
  
  
• EXAM 3-- Monday, December 4, 2017
  
  
• FINAL EXAM -- Friday, December 15, 2017, 8-10 am, 1001 Giedt
  
  

THE CALCULUS PAGE .

Here are some TIPS for doing well on my exams.

Here are instructions for an OPTIONAL EXTRA CREDIT survey and short paper

SCANNED PROBLEMS for Chapter 2 (Sections 2.1-2.6)


• HW #1 ... (Section 2.1) ... p. 64: 1-6, 15a, 17ab, 21a, 22a ... and ... Worksheet 1
  
  
• HW #2 ... (Section 2.2) ... p. 74: 1-6, 9, 10, 12, 15, 19, 21, 22, 24, 27, 30-33, 37, 38, 40, 44, 46, 48, 53, 57, 61, 64, 65, 80, 81a, 82, (Solve the next two problems using algebra.) 85, 87
  
  
• HW #3 ... (Section 2.4) ... p. 91: 2 (Omit j. and k.), 3, 7, 12, 15, 17b, 23, 24, 26, 27, 29, 34-36, 38-41, 45, 46, 52 (Use the Squeeze principle on problem 52b.) ... Here is a handout on Even and Odd Functions ... Here is a statement of and example of the Squeeze Theorem (Sandwich Theorem) ... Here is a derivation of a Special Trig Limit
  
  
• HW #4 ... (Section 2.6) ... p. 115: 1, 2, 4, 5, 8-10, 12-14, 16, 20 22, 23, 25-27, 30, 33, 34, 36, 37, 39, 42, 44, 49, 50, 54, 57, 59, (Use intercepts, vertical asymptotes, horizontal asymptotes, and tilted asymptotes to sketch graphs for each of the the following four problems.) 64, 67, 70, 71, 100, 104
  
  
• HW #5 ... (Section 2.5) ... p. 102: 2, 4-10, (For the next three problems clearly state and give brief reasons where each function is continuous.) 16, 20, 26, 29, 30, 42-44, 47, 48, 52 (This problem is optional.), 56, 59, 62, 63, (Use the IMVT for the following three problems to prove that the given equation is solvable.) 71, 74, 75 ... and I.) Use the IMVT to prove that x^3=x+2 has a solution. ... II.) Use the IMVT to prove that 2+ sin x = x has a solution. ... and ... Worksheet 2 ... Here is a handout on Continuity ... Here is a handout on the Intermediate Value Theorm (IMVT) and an Example using the IMVT.
  
  
• HW #6 ... (Section 2.3) ... p. 83: 7, 10, 11, 16, 17, 24, 39, 41, 47 ... Worksheet 3 ... Here is a handout and a detailed example of the Precise Epsilon/Delta Definition of Limit .

TYPES OF QUESTIONS FOR EXAM 1 FOR FALL 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

• 5 or 6 -- Compute Limits
• 1 -- Squeeze Principle
• 1 -- Domain and Range
• 1 or 2 -- Continuity
• 1 -- IMVT
• 1 -- Epsilon/Delta Proof
• 1 or 2 -- Asymptotes (horizontal, vertical, and/or tilted)
• 1 or 2 -- Others
• 1 -- OPTIONAL EXTRA CREDIT

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 AN 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 limit 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.

SOLUTIONS TO EXAM 1 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR FALL 2017 EXAM 1 IS :

A+ ...... 100-108

A ...... 90-99

A-/B+ ...... 85-89

B ...... 68-84

C ...... 50-67

D ...... 38-49

F ...... 0-37

SCANNED PROBLEMS for Chapter 3 (Sections 3.1-3.9)




• HW #7 ... (Section 3.1) ... p. 126: 1-3, 5, 8, 12, 18, 22-24, 26, 30, 32, 34, 35, 40, 41
  
  
• HW #8 ... (Section 3.2) ... p. 133: 1, 6, 8, 13, 16, 18, 22, 24-30, 32a, 35-37, 39, 41, 42, 44, 46, 47 ... and ... Worksheet 4
  
  
• HW #9 ... (Section 3.3) ... p. 144: 2, 7, 8, 14a, 16a, 17, 20, 23, 28, 31, 34, 39, 42, 43, 46, 51 (Change w=3z^2e^2z to w=3z^2e^z), 52, 54, 55, 57, 59, 61, 63, 64, 66a, 67-70, 75a, 77, 78 ... Here are proofs of the Product Rule and Quotient Rule.
  
  
• HW #10 ... (Section 3.4) ... p. 153: 1, 4, 7, 10-12, 15, 16, 20a, 21, 25, 26, 28, 29, 30a, 31 ... and the following problem: Find all points (x, y) on the graph of y = 4x-x^2 with tangent lines passing through the point (2, 5). The solution is Here ... Here are some ARC and IRC problems with solutions ... Here is a link explaining the concept of jerk .
  
  
• HW #11 ... (Section 3.5) ... p. 160: 1-3, 8-10, 12, 13, 15-17, 20, 22, 24, 34b, 36, 44 (Find points only.), 46-48, 52, 54, 58, 59, 61 ... Here is a short proof of the Derivative of sin x .
  
  
• HW #12 ... (Section 3.6) ... p. 168: (Use chain rule shortcuts. Do not simplify answers.) 9, 14, 15, 17, 18, 20, 22, 25, 28, 29, 33, 36, 38, 40, 43, 45, 48, 50, 52, 55, 58, 61, 63, 66 (Simplify answers for the next three problems.) 71, 74, 77, (Find only first derivative.) 78, 85, 86, 87cdeh, 89, 93, 94, (Assume that each month has exactlty 30 days that variable x represents days.) 98, 99, 100, 102, 103
  
  
• HW #13 ... (Section 3.7) ... p. 175: 1, 4, 6, 9, 11, 12, 15, 16, (Simplify answers for 21 and 26.) 21, 26, 28, 30, 31, 33, 38, 39, 41, 42, 44, 47, 51a, 53, 55, 56
  
  
• HW #14 ... (Section 3.8) ... p. 185: 2, 7, 8, 9, 11, 16, 19, 20, 22, 25, 28, 30, 32, 37, 39, 40, 51, 54, 59, 61, 65, 66, 68, 71, 74, 82, 85, 86, 90, 92, 93, 96 ... Here are some general notes on the Derivative of an Inverse Function and an example using male alligator eggs !!! ... Here is a proof of the Derivative of a Logarithm Function .
  
  
• HW #15 ... (Section 3.9) ... p. 192: 2, 3, 5, 7, 10-13, 15-18, 21, 24, 27, 29, 34, 36 (Simplify answers for the next three problems.) 39, 41, 42, 43-45 ... Here are formulas for the Derivatives of Inverse Trig Functions .

TYPES OF QUESTIONS FOR EXAM 2 FOR FALL 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

• 6 -- Differentiate Using Various Rules
• 1 -- Limit Definition of Derivative
• 1 -- Sketch f' from Graph of f
• 1 -- Implicit Derivatives
• 1 -- Sign Charts for f' and f''
• 1 or 2 -- Inverse Trig Derivatives
• 2 or 3 -- Others
• 1 -- OPTIONAL EXTRA CREDIT

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 HAVE ANOTHER STUDENT TAKE AN 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 limit and 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.

SOLUTIONS TO EXAM ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR FALL 2017 EXAM 2 IS :

A+ ...... 100-108

A ...... 90-99

A-/B+ ...... 84-89

B ...... 68-83

C ...... 46-67

D ...... 36-45

F ...... 0-35

SCANNED PROBLEMS for Chapter 3 (Sections 3.10 and 3.11) and Chapter 4 (Sections 4.1-4.5)


• HW #16 ... (Section 3.10) ... p. 198: 4, 5, 7-9, 11, 12, 15, 20-25, 27, 31-34, 36, 38-40, 41 (Change 8 inch diameter to 8 inch radius.) , 43a, 44 (HINT: Use the Law of Cosines.), 45 (Write your answer in degrees per minute.)
  
  
• HW #17 ... (Section 3.11) ... p. 211: 1, 3, 4, 5, 6, 15, 16acd, 17a, 40, 41, 43, 51-54, 56-59, 62 (Part a.) Use a differential to ESTIMATE the change in concentration. Part b.) Find the EXACT change in concentration.), 67a, 68a ... and ... Use differentials to estimate the exact values of (and a calculator to determine a percentage errors) ... 1.) .. sqrt{90} ... 2.) .. (2.0002)^{25} ... 3.) .. cos(0.01) ... 4.) .. ln(1.1) ... Here are brief notes on the Differential of a Function ... Here are examples using the differential to Estimate Functional Expressions and Percentage Error ... Here is a specific application of a differential in a Physics Example .
  
  
• HW #18 ... (Section 4.1) ... (Set up a sign chart for f ' to determine the absolute and relative maximum and minimum values of f.) p. 238: 23, 27, 37 (Change the interval from [-1,1] to [-1,2].), 39, 40, 44, 47, 48, 51, 53, 55, 57, 61, 63, 65, 66, (Use algebra only, no derivatives, to find the maximum and minimum values for the following two problems.) 87, 88
  
  ... and ... (Section 4.3) ... (Set up a sign chart for f ' to determine the absolute and relative maximum and minimum values of f. Also indicate the open intervals on which the function f is increasing and decreasing.) p. 242: 4, 5, 8, 14, 28, 33, 35, 36, 41, 54, 59, 60, 64, 73, 74, 75b, 76, 77
  
  
• HW #19 ... (Section 4.4) ... Here is a handout on Detailed Graphing using the first and second derivatives ... For all of the following problems use the Instructions for detailed graphing ... Here are some worked out Examples ... p. 252: 1, 2, 10, 17, 21, 23, 29, 30, 33, 41, 52, 58, 62, 66, 71, 77, 82, 83, 89, 93, 101, 102, 106, 112, 115, 120, 121,
  
  
• HW #20 ... (Section 4.2) ... p. 237: 1, 2, 5-9, 11, 13, 16, 23, 26, 33-42, 44, 46-48, 51, 52, 54, 56-58, 63, 65, 66, 73 ... Here is a cautionary Example using the MVT ... Here is a detailed handout outlining/proving Rolle's Theorem, the Mean Value Theorem , and other very important theorems. Please take a look at it, especially if you are a math major.
  
  
• HW #21 ... (Section 4.5) ... p. 262: 2, 4-7, 10, 13-15, 18, 20, 21, 24, 26, 27, 29, 32, 34, 35, 37-39, 41, 42, 44, 46-53, 56-60, 63, 64, 66, 67, 69, 72, 74, 79, 84ac, 86b, 87b, 88 ... Here is a brief handout showing the plausibility L'Hopital's Rule ... A detailed proof of L'Hopital's Rule using the Cauchy Mean Value Theorem can be found in your textbook.
  
  
• Believe it or not, here is an Extreme but Cool Example of a function which is CONTINUOUS for all x-values, but NOT DIFFERENTIABLE at any x-value !?@

TYPES OF QUESTIONS FOR EXAM 3 FOR FALL 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

• 3 -- Linearization/Differentials
• 2 -- Related Rates
• 2 or 3 -- Detailed Graphing (or specific parts of detailed graphing)
• 4 -- L'Hopital's Rule
• 1 -- MVT
• 1 or 2 -- Others
• 1 -- OPTIONAL EXTRA CREDIT

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 HAVE ANOTHER STUDENT TAKE AN 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.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT's EXAM.
• 3.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 4.) You will be graded on proper use of limit and derivative notation.
• 5.) Put units on answers where units are appropriate.
• 6.) 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.

SOLUTIONS TO EXAM 3 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR FALL 2017 EXAM 3 IS :

A+ ...... 100-110

A ...... 90-99

A-/B+ ...... 85-89

B ...... 68-84

C ...... 45-67

D ...... 35-44

F ...... 0-34

SCANNED PROBLEMS for Chapter 4 (Sections 4.6 and 4.7)


• HW #22 ... (Section 4.6) ... p. 270: 1, 2, 4, 5, 7, 9a, 11, 12, 14, 19, 20, 24, 25, 26-29, 33, 35, 36, 38, 39, 52, 56-58, 63, 66a, 67a, 68a ... Here are some Optional Max/Min Problems given without solutions.
  
  
• HW #23 ... (Section 4.7) ... p. 279: 2 (Estimate solution to 3 decimal places.), 3 (Estimate solutions to 3 decimal places.), 5, 8-10, 13, 18, 21 (Estimate solutions to 3 decimal places.), 29 (Find x1, x2, and x3.), 30

The FINAL EXAM is

8-10 am

Friday, December 15, 2017

in 1001 Giedt

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

The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 23, material from sections 2.1-2.6, 3.1-3.11, 4.1-4.7, and discusssion sheets 1-10.

TYPES OF QUESTIONS FOR THE FINAL EXAM FOR FALL 2016 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.).

• 4 or 5 -- Limits
• 1 -- Domain and Range
• 1 -- Continuity
• 1 -- Epsilon, Delta Proof
• 1 -- Implicit Differention
• 1 -- Differential
• 1 or 2 -- Related Rates
• 1 -- Detailed Graphing
• 1 -- Newton's Method
• 3 -- Applied Maximum/Minimum
• 1 or 2 -- Others
• 1 or 2 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR THE FINAL EXAM.

• 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 HAVE ANOTHER STUDENT TAKE AN 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.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT's EXAM.
• 3.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 4.) You will be graded on proper use of limit and derivative notation.
• 5.) Put units on answers where units are appropriate.
• 6.) 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.

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Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address :

kouba@math.ucdavis.edu .