• HW #16 ..... p. 590: 1, 2, 3, 6, 7, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 22, (For the next two problems, write the answers as a mixed fractions.) 23, 25, 28, 29, 31 (challenging), 33ab, 34b (optional)
  
  
• HW #17 ..... p. 596: 1, 3, 4, 5, 6, 7, 10, 12, 13ab (On part b Use equation (*) from handout in class and let n go to infinity.), 14 (Use cases on p. Let 0 < p < 1, p=1, p=0, and p<0.), 16, 18, 20, 21, 26 (HINT: Consider the graph of f(x)=1/sqrt(x) for x>or=1 and use equation (*) from handout in class.), (Use equation (*) from handout in class.) 27, 28b, 30 (optional)
  
  
• HW #18 ..... p. 601: 1-8, 10, 11, 13, 15-18, 20, 21, 23-34, 36 (challenging), 39a, 41 (optional), 43, 44
  
  
• HW #19 ..... p. 605: 1-8, 13, 14, (Use equation (*) on problems 16, 20, 22, and 23.) 16, 20, 22, 23, 26.
  
  
• HW #20 ..... p. 615: 1-10, 28, 30, 31, 39
  
  
• HW #21 ..... p. 615: 11-25

TYPES OF QUESTIONS FOR EXAM 3 2005 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.).

• 8 -- determine if given series converges or diverges
• 1 -- estimating partial sum (equation (*)) or estimating error (equation (*)(*))
• 1 -- question about alternating series
• 1 -- other
• 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 3.

• 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 2.) You will be graded on proper use of derivative and integral notation.
• 3.) Put units on answers where units are appropriate.
• 4.) 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.

SOLUTIONS TO EXAM 3 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR 2005 EXAM 3 IS :

A+ ...... 100-112

A ...... 88-99

A-/B+ ...... 84-87

B ...... 70-83

C ...... 51-69

D ...... 41-50

F ...... 0-40

• HW #22 ..... p. 648: 1, 2, 3, 4, 7, 10, 11, 12, 14, 15, 16, 18, 19, 22, 24, 26, 33, 34
  
  
• HW #23 ..... p. 628: (Find 1st four nonzero terms and general formula for the Maclaurin series on the next 4 problems.) 13, 15, 17, 18, 2 (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=1 for f(x)= 1/(1+x).), 3 (Use problem 13.), 6 (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=2 for f(x)=e^x.), 10 (Use class notes.), 22, 27ab (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=0 for f(x)=sqrt(1+x). On part b use interval [-2, 2].), 34 (Let n=4)
  
  
• HW # 24 ..... p. 635: (Use the Lagrange form of the Taylor remainder on problems 1 and 2.) 1, 2, 7 (Use the absolute error |Rn| for an alternating series and use an error of at most 0.0005.), {{{ Problem A: Use the Maclaurin series for f(x)=cos(x) (See problem 15 on page 628.) to estimate the value of cos(1) with absolute error at most 0.0001., Problem B: If we use the Maclaurin series for f(x)=ln(1+x) (See problem 13 on page 628.), how many terms should be used to estimate the value of a.) ln(2) with absolute error at most 0.001 ? b.) ln(1.5) with absolute error at most 0.001 ? }}}, 8 (Use the Lagrange form of the Taylor remainder and make it at most 0.0005.), 14 (Use the Maclaurin series for cos(x), the absolute error |Rn| for an alternating series, and use an error of at most 0.0005.)
  
  
• HW # 25 ..... p. 655: 3 (On d. use an absolute error of at most 0.0005.), 6, 7, 8, 9, 11, 14, 15 (On b. use an absolute error of at most 0.00005.), 25 ..... and ..... p. 674: 18 (Use the Lagrange form of the remainder.), 19 (Use the absolute error |Rn| for an alternating series.), 33ad (Use the absolute error |Rn| for an alternating series.), 49 (You need not use L'Hopital's Rule.), 51 (First write the power series as an ordinary function, then differentiate.)
  
  
• HW # 26 ..... p. 664: 1ad, 2ad, 3ab, 5, 6, 7abcd, 11, 12, 13, 14, 19degh, 20d, 23, 36, 21, 10.... Here are Class Notes for this section (Section 11.6).
  
  
• HW # 27 ..... p. 670: 1, 6, 9, 17, 18, 23, 25, 26.... Here are Class Notes for this section (Section 11.7).
  
  
  
  

  The FINAL EXAM is Thursday, June 16, 2005,
  
  

  8 a.m.-10 a.m. (7:30-10:15 a.m. ?)
  
  
  

  in 1100 Social Sciences
  
  
  
  

  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 (Homework assignments 26 and 27 are optional), and material from sections 14.1-14.6, 14.9, 15.1-15.7, 10.1-10.7, 11.1, 11.2, 11.4, 11.5 (11.6 and 11.7 are a source of problems for the extra credit problems on the final exam), and discusssion sheets 1-11.
  
  

  TYPES OF QUESTIONS FOR THE FINAL EXAM 2005 (THIS LIST IS TENTATIVE AND IS SUBJECT TO UNANNOUNCED CHANGES.).
  
  

  • 2 -- limits for functions f(x,y)
  • 1 -- interval of convergence
  • 1 -- three dimensional graphing
  • 1 -- triple integral
  • 1 -- partial derivatives
  • 1 -- using (*) or (**)
  • 2 -- find Maclaurin series using shortcuts
  • 1 -- conditionally convergent, absolutely convergent, divergent
  • 1 -- find Taylor series using f^(n)(a)/n!
  • 1 -- find Taylor polynomial of degree n
  • 1 -- find and classify critical points for z=f(x,y)
  • 1 -- use Lagrange form of Taylor error, Rn(x;a)
  • 2 -- others
  • 3 -- OPTIONAL EXTRA CREDIT (ON ANY TOPIC)
  
  
  

  HERE ARE SOME RULES FOR THE FINAL EXAM.

  • 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
  • 2.) You will be graded on proper use of limit notation.
  • 3.) You will be graded on proper use of derivative and integral 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 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 .