Calculus I Review Problems (pdf file)
Section 7.2 Homework: #13, 17, 21, 25, 29, 33, 37, 39, 43, 47,
51
Quiz #1 on this material will be Tuesday, August 29 at the beginning of class.
Although you will not be turning in these problems, you should write out the
solutions as if you were!
Section 7.3 Homework: #1,2 (answer 1/2 x^2 e^(2x) - 1/2 x e^(2x) + 1/4 e^(2x) +C), 3, 5, 7, 13, 15 (an alternative to integration by parts is substitution - see problems 31-35 from 7.2), 31, 35, 49, 55
Quiz #2 on 7.3 and 7.4 is Tues. Sept. 5.
A website with some additional practice problems and solutions:
http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/intbypartsdirectory/IntByParts.html
Section 7.4 Homework: #1, 3, 5, 6, 7, 8, 10, 11, 13, 17, 25,
27, 30, 37
Note: some changes were made to the assignment on
8-30-06. This is the updated list of problems.
Quiz #2 on 7.3 and 7.4 is Tues. Sept. 5.
Note: I've assigned some even-numbered problems because there aren't any
similar even-numbered examples. Be sure to take a look at these before recitation so you can check the answer
with your TA if you're not sure.
This material is difficult. Do extra practice! In
Section 7.6 we’ll be using the Section 7.4 techniques.
A website with some additional practice problems and solutions:
http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html
Section 7.5 Homework: #1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 25,
27, 37, 41, 49, 59
These problems take some time - don't wait until the last minute!
Quiz #3 on 7.5 is Tues. Sept. 12.
More practice:
http://archives.math.utk.edu/visual.calculus/4/partial_fractions.1/
Section 7.6 Homework: #1, 3, 5, 9, 15, 23, 26, 29, 33
Quiz #4 on 7.6 and 7.7 is Tues. Sept. 19.
Hints:
*In problem 29, use the trig identity tan^2 = sec^2 -1 to find the antiderivative of tan^2.
*In problem 33, after you've done the trig substitution, convert everything
into sin and cos in order to find the antiderivative.
*To master trig substitutions, you may need more practice than just these
homework problems. Here are two websites with some more practice problems
and solutions:
http://archives.math.utk.edu/visual.calculus/4/substitutions.2/
http://online.math.uh.edu/Math1432/Section8.4/TrigSub/TrigSubPract.html
Section 7.7 Homework: #1, 3, 5, 7
Quiz #4 on 7.6 and 7.7 is Tues. Sept. 19.
Section 7.8 Homework: #1, 3, 5, 11, 17, 20, 21, 27, 29, 35, 43, 44
Note: #20 at first appears to be a proper integral, but it is not, because the integrand is undefined for x=1. You'll need to first split it into two improper integrals, one from 0 to 1 and the other from 1 to 2. Both of these diverge, so the original integral diverges.
Quiz #5 on 7.8 is Thurs. Sept. 21
Section 10.2 Homework: From Concepts: Questions and Discussion on page 691, do 1, 2, 3. From the problems, do # 1, 4, 5, 9, 11, 13, 15, 19, 25, 29, 33
Quiz #6 on 10.1, 10.2, 10.3 is Tues. Oct. 3 (no quiz on Tues. Sept. 26)
See http://archives.math.utk.edu/visual.calculus/6/index.html for more practice on all the topics in Chapter 10.
Section 10.3 Homework: From Concepts: Questions and
Discussion on page 701, do 2, 3,
4. From the problems, do #1, 3, 5, 7, 9, 15, 25, 31, 45, 47, 61
Quiz #6 on 10.1, 10.2, 10.3 is Tues. Oct. 3 (no quiz on Tues. Sept. 26)
Section 10.4 Homework: From the problems, do #1, 3, 5, 13, 15, 19, 23, 27, 31, 39
Quiz #7 on 10.4 is Tues. Oct. 10
Section 10.5 Homework: From Concepts: Questions and Discussion on page 722, do 1, 2. From the problems, do # 1, 7, 11, 13, 31, 33, 35 (geometric - don't use integral test!), 37, 39, 43
Note: For the answer to problem #11, the book uses the integral from 0 to infinity. It would make more sense to use the integral from 1 to infinity, since the series starts with n=1.
Quiz #8 on 10.5 and 10.6 is Tues. Oct. 17
See http://archives.math.utk.edu/visual.calculus/6/index.html for more practice on all the topics in Chapter 10.
Section 10.6 Homework: From Concepts: Questions and Discussion on page 729, do 1, 3. From the problems, do #1, 3, 9, 17, 21, 27, 31, 33, 37. It is advisable to do additional practice - any of the problems 1-36 are good practice.
Quiz #8 on 10.5 and 10.6 is Tues. Oct. 17
Section 10.7 Homework: From Concepts: Questions and Discussion on page 737, do 1, 3. From the problems, do #1, 3, 5, 13, 21, 22, 23, 24, 25, 27, 30, 31, 32, 34, 39, 43, 49
Answers to even problems:
(22) converges absolutely; comparison test with 1/(n^2)
(24) converges absolutely; root test or comparison test with 1/(n^2)
(30) converges absolutely; ratio test
(32) diverges; root test
(34) converges absolutely; ratio test
Quiz #9 on 10.7 is Tues. Oct. 24
Section 10.8 Homework: Problems #1, 3, 5, 7, 15, 17, 19, 29, 31, 33, 35, 43, 45, 49. It is advisable to do even more practice - any of the problems 1-51 would be good practice.
Quiz #10 on 10.8 and 10.9 is Tues. Oct. 31
Section 10.9 Homework: Problems #1, 3, 11, 15, 17, 23, 25, 33, 34, 37
Correct answer to #11 is .9461 and correct answer to #37 is 1.40, which may differ from the answer in the back of your book.
Quiz #10 on 10.8 and 10.9 is Tues. Oct. 31
Section 6.4 Homework: Problems #5, 7, 9, 23, 29, 31
Quiz #11 on 6.4 and 8.1 and 9.1 9.2 is
Tues. Nov. 14 (no quiz on Tues. Nov. 7, but class will meet as usual.)
Section 8.1 Homework: Problems #1, 3, 5, 7, 9, 33
Quiz #11 on 6.4 and 8.1 and 9.1 9.2 is Tues. Nov. 14 (no quiz on Tues. Nov. 7, but
class will meet as usual.)
Section 9.2 Homework: Problems # 1, 2, 3, 6, 7, 9, 11, 12, 13, 18; 19, 25, 29, 31, 33, 39, 41, 43, 45, 47, 50, 53
Note: This assignment has a lot of problems! In order to learn to
work with polar coordinates, you need lots of practice.
Quiz #11 on 6.4 and 8.1 and 9.1 9.2 is
Tues. Nov. 14
You can print out free polar graph paper here:
http://www.mathematicshelpcentral.com/graph_paper.htm
http://mason.gmu.edu/~mmankus/Handson/polar.htm
Section 9.3 Homework: #1, 7, 9, 17, 21, 25, 29, 35
Suggestion: Sketch the graph for each problem
Quiz #12 on 9.3 and 9.4 is Tues. Nov. 28
Section 9.4 Homework: #1, 3, 7, 13, 15, 17, 19, 25, 27a, 29
Quiz #12 on 9.3 and 9.4 is Tues. Nov. 28
Section 9.5 Homework: #1, 2, 3, 7, 8, 9,
11, 13, 17, 18, 25
Quiz #13 on 9.1, 9.5, 9.6 is Thursday, Dec. 7. This quiz is optional. If you
take it, your grade on quiz #13 will replace your lowest quiz grade.
Section 9.1 Homework: #9, 13
Quiz #13 on 9.1, 9.5, 9.6 is
Thursday, Dec. 7. This quiz is optional. If you take it, your grade on quiz #13
will replace your lowest quiz grade.
Section 9.6 Homework: #1-15 odd, 19, 21, 23, 35, 37, 39, 41, 43, 53, 55
Quiz #13 on 9.1, 9.5, 9.6 is
Thursday, Dec. 7. This quiz is optional. If you take it, your grade on quiz #13
will replace your lowest quiz grade.