MATH 17A (SECTIONS A001-A005), 2205 Haring, 11-11:50 MWF (T Disc)

Instructor: Dr. D. A. Kouba

Text: CALCULUS for Biology and Medicine (3rd edition) by Claudia Neuhauser

Office: 3135 MSB (Mathematical Sciences Building)

Phone: (530) 752-1083

Office Hours: Variable (announced in class) or by appointment

Please read the Mathematics Placement REQUIREMENTS to enroll in Math 17A.

• ...... Here is a list of Exam ID Numbers .
  
  
• ...... MATH 17A FINAL COURSE GRADES (listed by last five digits of student ID number).

• EXAM 1-- MONDAY OCTOBER 18, 2010
  
  
• EXAM 2-- FRIDAY, NOVEMBER 5, 2010
  
  
• EXAM 3-- MONDAY, NOVEMBER 22, 2010
  
  
• FINAL EXAM -- TUESDAY, DECEMBER 7, 2010, 10:30 a.m. - 12:30 p.m., in 2205 Haring

Here are Math 17A ... HOMEWORK Solutions . . . and . . . EXAM Solutions .

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 .

These are the OPTIONAL EXTRA CREDIT survey and short paper .

SCANNED PROBLEMS for Chapter 1


• HW #1 ... (Section 1.1) ... p. 13: 3ab,4a, 5ab, 8, 12, 15, 18, 20, 25, 28, 30, 31, 44, 46, 47, 51, 52, 55, 59, 62, 63, 65, 67, 71, 74ab, 75ab, 77abc, 81a, 82b, 84c, 87, 90, 102
  
  
• HW #2 ... (Section 1.2) ... p. 34: 1, 2, 7, 8, 12, 16, 31, 33, 36, 56, 58, 69bcd, 70, 75, 81bde, 82adf, 83c, 84d, 99
  
  
• HW #3 ... (Section 1.3) ... p. 52: 1, 2, 5, 6, 8, 9, 11, 15, 17, 23, 30, 100
  
  SCANNED PROBLEMS for Chapter 2
  
  
• HW #4 ... (Section 2.1) ... p. 67: 1, 4, 5-9, 12, 13, 17, 20, 22, 26, 29, 37, 42, 47, 54
  
  
• HW #5 ... (Section 2.2) ... p. 78: 2, 9, 10, 19-22, 26-31, 34, 38, 39, 43, 45, 49, 50, 54, 61, 66, 68, 70, 72, 75, 78, 81, 83, 88, 91, 93, 96, 100, 105, 106, 109 ... and ... Epsilon,N Proof Worksheet
  
  
• HW #6 ... (Section 2.3) ... p. 8: 1, 3, 6, 8, 9, 12, 14, 15, 20, 21, 24, 55, 57 (Make a conjecture about the behavior of Nt/Nt-1 as t gets large.)
  
  SCANNED PROBLEMS for Chapter 3
  
  
• HW #7 ... (Section 3.1) ... (Use arithmetic and algebra as done in class to write solutions to limit problems) p. 101: 2, 3, 6, 7, 9, 10, 11, 13, 21, 23, 24, 26, 28, 29, 32, 34 (Use algebra and approved shortcuts.), 36, 41, 47, 49, 50, 54
  
  
• HW #8 ... (Section 3.2) ... p. 108: 3, 5, 7 (Insert f(x)=a if x=3.) , 8-12 ... and ... Worksheet 1
  
  
• HW #9 ... (Section 3.3) ... p. 113: 1-3, 8-10, 13-16, 18-24, 27, 29

TYPES OF QUESTIONS FOR EXAM 1 FOR FALL 2010 (subject to change)

• 4-- Various Limits
• 1-- Domain and Range of Function
• 1-- Recursion, Initial Value, Exponential Growth/Decay Problem
• 1-- Continuity
• 1-- Epsilon/N Proof
• 1-- Find Fixed Points for Recursion
• 2-- Find Formula for Sequence
• 1-- Beverton-Holt Recursion
• 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 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.) Using only a calculator to determine the value of limits will receive little 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.

THE GRADING SCALE FOR EXAM 1 FOR FALL 2010 IS :

A+ ...... 100-110

A ...... 90-99

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

B ...... 70-84

C ...... 50-69

D ...... 38-49

F ...... 0-37

• HW #10 ... (Section 3.4) ... p. 118: 1, 4ac, 5-16, 19, 20
  
  
• HW #11 ... (Section 3.5) ... p. 122: 2, 4, 5, 7, 9a(first use the IMVT to prove that the equation is solvable. Change the function from 3x^3-4x^2-x+2 to 3x^3-4x^2-x+3) ... Complete the Bisection Method in the following TABLE by assuming that f(x)=ln(x+1)+x-1 is solvable on the interval [0, 1] and estimating the value of the solution to two decimal places.
  
  SCANNED PROBLEMS for Chapter 4
  
  
• HW #12 ... (Section 4.1) ... (Use the limit definition to compute all derivatives.) ... p. 143: 1, 2, 5, 10,13, 21, 23a, 24a, 25, 26, 30, 35, 38, 39, 42 (Assume that s'(t)=3-2t.), 49, 51, 58, 64, 67, 68 ... and ... Worksheet 2
  
  
• HW #13 ... (Section 4.2) ... p. 149: 1, 4, 6, 10, 16, 18-20, 25, 30, 32, 37, 44, 50, 60, 64, 67, 69, 73, 75, 78 (Note that the point (0,-1) is NOT on the graph of y=x^2.), 80 (Note that the point (-1/2,-3) is NOT on the graph of y=x^2+2x.)
  
  
• HW #14 ... (Section 4.3) ... p. 158: 1, 4, 6, 9, 17, 23, 26, 28, 35, 36, 38, 43, 47, 48, 49, 52, 65, 72, 73, 83, 87, 94
  
  
• HW #15 ... (Section 4.4) ... p. 172: 2, 5, 9, 12, 16, 17, 19, 24, 27, 34a, 35b, 37, 38, 43, 47, 48, 50-55, 60a, 61, 63, 65, 69-71, 74, 80, 86ab ... and ... Gravity Problems ... and ... Here a link describing the meaning of jerk as an application of the third derivative.

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. (Chain Rule) D f(g(x)) = f'(g(x)) g'(x)

TYPES OF QUESTIONS FOR EXAM 2 FOR FALL 2010 (subject to change)

• 3 -- Use Rules of Differentiation
• 1 -- Intermediate Value Theorem
• 1 -- Limit Definition of Derivative
• 1 -- Bisection Method
• 1 -- ARC (Average Rate of Change)/IRC (Instantaneous Rate of Change)
• 1 -- Implicit Differentiation
• 1 -- Related Rates
• 1 -- Sketch Graph of f' Using Graph of f
• 1 or 2 -- 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 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 need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
• 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 and derivative 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.

THE GRADING SCALE FOR EXAM 2 FOR FALL 2010 IS :

A+ ...... 100-110

A ...... 90-99

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

B ...... 70-84

C ...... 55-69

D ...... 40-54

F ...... 0-39

• HW #16 ... (Section 4.5) ... p. 177: 1, 5, 6, 9, 11, 13, 14, 17-19, 21, 24,27-29, 32, 37, 41, 44, 46, 48, 51, 55, 56, 57, 59 (on interval [0, 2 pi]), 60 (on interval [0, 2 pi]), 63, 65, 69, 70, 71, 73 (on interval [0, 4])
  
  
• HW #17 ... (Section 4.6) ... p. 181: 1, 4, 8, 9, 11, 13, 14, 17, 20, 21, 24, 29, 33, 37, 42, 49, (Use the limit definition of the derivative to solve problems 53-56.) 53-56, 59, 60, 61, 64, 70, 71, ... Find more information about carbon dating here and here ... (For the following two problems assume that dW/dt=kW for radioactive decay, so that W=W(0) e^{kt}, where W(0) is the initial amount of radioactive material.)72, 73 ... and ... I. Initially, a bacterial culture weighs 50 grams. In 4 hours it weighs 85 grams. Assuming exponential growth, find the growth equation for this culture. a.) What is the mass of the culture in 6 hours ? b.) When will the culture have a mass of 200 grams ? ... II. The half-life of radioactive radium is 1600 years. If a sample containing 20% of the original amount remains, how old is the sample ? ... and ... III. Estimate the percentage of carbon-14 in Kwaday Dan Sinchi by assuming he died in 1400 and the half-life of carbon-14 is about 5730 years.
  
  
• HW #18 ... (Section 4.7) ... p. 192: 2, 5, 7, 11, 15, 26, 31, 34, 36, 37, 45-47, 49, 51, 58, 60, 63, 67, 71-73, 76
  
  
• HW #19 ... (Section 4.8) ... p. 198: 2, 3, 9, 11, 17, 22, 32, (Use the differential for the remaining problems.) 37, 38, (Only estimate the maximum absolute % error for f in the next 3 problems.) 41, 43, 44, 45, 46
  
  SCANNED PROBLEMS for Chapter 5
  
  
• HW #20 ... (Section 5.1) ... p. 213: 35, 36, 38, 40, 41, 44, 48, 55
  
  
• HW #21 ... (Section 5.2) ... (Do Detailed Graphing using these INSTRUCTIONS for the first nine problems.) p. 222: 2, 6, 7, 10, 14, 15, 17, 19, 20, 29, 30, 33, 42
  
  
• HW #22 ... (Section 5.3) ... (Do Detailed Graphing using these INSTRUCTIONS for all problems.) p. 235: 1, 2, 7, 12, 14, 16, 22 (Assume domain is all x-values. Assume that limit (x to infinity) of x/e^x is 0.), 28, 33, 36, 37 (Rewrite the function to be f(x)= (2x^2-6)/(x+2). Note that oblique asymptote means the same as tilted asymptote.)
  
  
• HW #23 ... (Section 5.4) ... p. 243: 1, 3-6, 9, 11ab, 13, 17, 19a ... and ... Worksheet 3 ... ( Worksheet 3 Solutions )

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. (Chain Rule) D f(g(x)) = f'(g(x)) g'(x)
10. D e^x = e^x
11. D a^x = a^x ln a
12. D ln x = 1/x
13. D log_b x = (1/x) (1/ln b)
14. D(sin x) = cos x
15. D(cos x) = - sin x
16. D(tan x) = sec^2 x
17. D(sec x) = sec x tan x
18. D(cot x) = - csc^2 x
19. D(csc x) = - csc x cot x

TYPES OF QUESTIONS FOR EXAM 3 FOR FALL 2010 (subject to change)

• 4 -- Use Rules of Differentiation
• 1 -- Linearize Function or Use Linearization to Estimate Value of Number
• 1 -- Use Differentials to Estimate Absolute Percentage Error
• 1 -- Derivative of Inverse Function
• 1 -- Exponential Growth/Decay
• 1 -- Mean Value Theorem
• 2 or 3 -- Complete Detailed Graphing or Parts of Detailed graphing
• 2 or 3 -- Maximum/Minimum Problems
• 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 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.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. 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.
• 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 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.

THE GRADING SCALE FOR EXAM 3 FOR FALL 2010 IS :

A+ ...... 100-110

A ...... 90-99

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

B ...... 70-84

C ...... 48-69

D ...... 35-47

F ...... 0-34

• HW # 24 ... (Section 5.5) ... p. 252: 2, 3, 6-9, 11, 13, 14, 15, 19-21, 23, 24, 26, 30, 33, 35, 37, 38, 40, 42-44, 49, 52, 58, 60, 61, 63, 66 (Assume that a=1.)
  
  
• HW # 25 ... (Section 5.7) ... (Find solutions to THREE decimal places for problems 1, 3, and 5.) p. 266: 1 (Assume x>0.), 3, 5, 6, 8a
  
  
  
  

  The FINAL EXAM is Tuesday, December 7, 2010,
  
  

  10:30 a.m. - 12:30 p.m.
  
  
  

  in 2205 Haring
  
  
  
  

  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 25, and material from sections 1.1-1.3, 2.1-2.3, 3.1-3.5, 4.1-4.8, 5.1-5.5, 5.7. You are expected to know the 17 rules of differentiation, which were needed on Exam 2. Use your three hour exams, 24 homework assignments, and discussion sheets as a guide to your preparing for the final exam.
  
  

  TYPES OF QUESTIONS FOR THE FINAL EXAM FOR FALL 2010 (subject to change)

  • 3 -- Limits Using L'Hopital's Rule
  • 1 -- Limit Definition of Derivative
  • 1 -- Finding Horizontal, Vertical, or Tilted Asymptotes
  • 1 -- Projectile/Gravity Problem
  • 1 -- N/Epsilon Proof for Limit of a Sequence
  • 1 -- Detailed Graphing
  • 1 -- Exponential Growth/Decay
  • 1 -- Linearization
  • 1 -- Differential
  • 2 -- Maximum/Minimum
  • 1 -- Related Rate
  • 1 -- IMVT/Newton
  • 1 -- Implicit Differentiation
  • 3 -- Others
  • 1 -- 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 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 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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Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address :

kouba@math.ucdavis.edu .