### Homework

• See the syllabus for full details on written homework.
• Homework, quiz and tutorial grading questions should be directed to your TA:
Kevin Selker ( kevin.selker at colorado edu / Math Office 342 ).

### Homework Help

• Here are my tips on doing mathematics homework.

### Written Homework Assignments

• Due Thursday, September 6th:
7.1   24, 70, 72, 86 (note: these are some harder substitutions; do the easier ones on webwork first if you are having trouble);
8.1  12, 27 (for this problem, please slice the water into horizontal slices and do an integral; then compare to a simpler geometric method to compute the volume!);
8.2  7, 29, 36.
Extra problem: Compute the volume of a 5-dimensional sphere, using the formula for the volume of a 4-dimensional sphere. Solution here.
SOLUTIONS: click on each number above.
• Due Thursday, September 13th:
7.2   1, 22, 23, 26 (note: these are some harder integration-by-parts problems; do the easier ones on webwork first if you are having trouble);
8.2  14
8.3  12, 15, 16, 25, 31, 34, 41, 42.
SOLUTIONS: click on each number above.
• Due Thursday, September 20th:
7.7   8, 12, 16, 36, 43, 50;
Extra Problem 1: Find the antiderivative of xnex, where n is a positive integer. That is, figure out what the answer looks like as a formula depending on n. Hint: Do a few small cases to figure out the general pattern. Explain what you do.
Extra Problem 2: Suppose that every undergraduate at CU takes a True-False test by guessing. How many questions does the test need to have so that the expected number of perfect scores is closest to 1? What about if it is a multiple choice test where each problem has 5 options? For the multiple choice test, do you still expect the scores on the test to be distributed as a bell curve (hint: play with the quincunx)? What is the average grade?
SOLUTIONS: click on each number above (solutions to extra problems here).
• Due Thursday, September 27th:
7.4   16, 19, 43, 44
7.8   2, 6, 18, 24, 28, 30
Chapter 7 "Check Your Understanding" (p. 389)   17-20.
• Due WEDNESDAY, October 3rd:
Note the due date one day early!
NOTE: This is a large assignment, and it will count double: once for a Written Homework and also a Webwork (it replaces the Webwork due Monday the 1st).
8.4   3, 8, 11, 28.
Chapter 7 Review   26, 42, 66, 92, 126, 127, 153, 169, 174 (all these can be done by hand with the methods we've learned).
Chapter 8 Review   5, 19, 28, 41, 47, 49, 50, 51, 52, 53.
The idea is to use this assignment as review for the midterm. When you hand it in, keep a photocopy for yourself and check your own answers against the solutions, which will be posted at 10am on Wednesday. More suggested review problems are on the Resources page.
• Due Thursday, October 11th:
9.1   42, 43, 45, 52, 55
9.2   3, 7, 12
Extra Problem: If a sequence is given by recursive formula Sn = 2Sn-1 + 3Sn-2, and S3 = 9 and S4=27, then a) what are S1 and S2; and b) what is a closed form for Sn? Check that your closed formula works for the first four terms. Finally, think back to the tutorial, where we used a recursive formula to verify a closed formula by checking that if the closed formula is true for term Sn, then it is true for term Sn+1. Use the same method here to prove your closed formula is correct. This method is called induction.
Solution to extra problem here.
• Due Thursday, October 18th:
9.2   20, 25, 36, 37(b) (you may use the result of 37(a) )
9.3   10-12, 18, 19, 26, 34, 37
9.4   6, 15, 30, 32, 36
• Due Thursday, October 25th:
9.5   11, 13, 21, 24, 32
10.1   5, 6, 14, 17, 24, 25, 28(a), 29
• Due Thursday, November 1st:
10.2   29, 30, 32
10.3   4, 19
10.4   7, 21
Extra Problem:   Find all power series which are equal to their own derivative (i.e. write down a general power series and determine what has to be true about its coefficients; using this, explain what is the full set of solutions).
• Due WEDNESDAY, November 7th:
Note the due date one day early!
NOTE: This is a large assignment, and it will count double: once for a Written Homework and also a Webwork (it replaces the Webwork due Monday the 5th).
Chapter 9 Review: 1, 3, 5, 6, 30, 31, 34, 36, 37, 41, 43, 45, 47, 54, 58, 71, 72, 76-80
Chapter 9 Check Your Understanding: 2, 7, 8, 12, 20, 28, 44 (for `Check Your Understanding' questions, provide a justification for why the answer is True/False)
Chapter 10 Review: 3, 12, 17, 21, 28, 30, 32, 34 (note: think before finding a series the 'direct' way; it may be easier to use one of the methods we've seen)
Chapter 10 Check Your Understanding: 20, 22-24
The idea is to use this assignment as review for the midterm. When you hand it in, keep a photocopy for yourself and check your own answers against the solutions, which will be posted at 10am on Wednesday. More suggested review problems are on the Resources page.
• Due Thursday, November 15th:
11.2   1,2,4,6,10,11,12; for some of these you will need to draw on the slope fields: you can find printable versions of these fields here (please make sure you use the right one for the right problem! compare with your text). Problem 1: A color, A black-white (note! solutions are in the back of the book; draw *different* curves (there are infinitely many to choose from) for full credit, Problem 4: B color, B black-white, Problem 11: C color, C black-white (if you use the black-white versions, please draw with a color pen);
11.4   6,12,20.
• Due Thursday, November 29th:
11.4   24;
11.5   2, 4, 6, 16, 24;
12.1   4;
12.2   2, 4, 6, 8, 14, 22, 24;
• Due Thursday, December 6th:
12.3   2, 4, 10, 14, 16, 25 (for this one, please make different choices of slices than the back of the book);
14.1   6, 16, 20;
14.2   2, 12, 28, 34, 38;
• Due Thursday, December 13th:
NOTE: This is a large assignment, and it will count double: once for a Written Homework and also a Webwork (it replaces the Webwork due Monday the 10th).
Chapter 11 Review   2, 4, 8, 20, 22, 34, 40;
Chapter 12 Review   6, 8, 12, 14, 16, 32, 34;
Chapter 12 Check Your Understanding   34, 36;
Chapter 14 Review   10, 14, 60;
Chapter 14 Check Your Understanding   9, 15;
Chapter 16.2   32, 36, 44;
Chapter 16 Review   6, 13, 16;