Calculus I Review Problems (pdf file) - due Thursday January 19 at the beginning of class. This will count as your first quiz grade.
Section 7.2 Homework: #13, 17, 21, 25, 29, 33, 37, 39, 43,
47, 51
There will be a quiz on this material on Tuesday, January 24 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, 39, 49, 55
(39 has been removed since some of you did not do volume by shells in Calc. I)
Quiz on 7.3 and 7.4 is Tues. Jan. 31.
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, 27, 36, 37
Quiz on 7.3 and 7.4 is Tues. Jan. 31.
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.
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 on 7.5 and 7.6 is Tues. Feb. 7
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 on 7.5 and 7.6 is Tues. Feb. 7
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 on 7.7 and 7.8 is Tues. Feb. 14.
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 on 7.7 and 7.8 is Tues. Feb. 14.
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 on 10.2, 10.3 is Tues. Feb. 28. There is no quiz on Tues. Feb. 21, but recitation classes will meet as usual.
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 on 10.2, 10.3 is Tues. Feb. 28. There is no quiz on Tues. Feb. 21, but recitation classes will meet as usual.
Section 10.4 Homework: From the problems, do #1, 3, 5, 13, 15, 19, 23, 27, 31, 39
Quiz on 10.4 and 10.5 will be Tues. March 7.
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 on 10.4 and 10.5 will be Tues. March 7.
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 on 10.6 and 10.7 will be Tues. March 14.
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 on 10.6 and 10.7 will be Tues. March 14.
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 on 10.8 will be Tues. March 28.
Section 10.9 Homework: Problems #1, 3, 11, 15, 17, 23, 25, 33, 34, 37
Quiz on 10.9 and 6.4 will be Tues. April 11. (no quiz Tues. April 4 because of Test #2 on April 3)
Section 6.4 Homework: #4, 5,11, 12, 13, 15, 19, 21, 25, 29, 31
Quiz on 10.9 and 6.4 will be Tues. April 11.
Section 8.1 Homework: #1, 3, 5, 7, 9, 33
Quiz on 8.1 and 9.2 will be Tues. April 18.
Section 9.2 Homework: #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 on 8.1 and 9.2 will be Tues. April 18.
Section 9.3 Homework: #1, 7, 9, 17, 21, 25, 29, 35
Suggestion: Sketch the graph for each problem.
Quiz on 9.3 and 9.4 will be Tues. April 25
Section 9.4 Homework: #1, 3, 7, 13, 15, 17, 19, 25, 27a, 29
Quiz on 9.3 and 9.4 will be Tues. April 25
Section 9.5 Homework: #1, 2, 3, 7, 8, 9, 11, 13, 17, 18, 25
Quiz on 9.5 and 9.6 (parabolas only) will be Tues. May 2
Section 9.6 Homework: #1-17 odd on parabolas. Also #19, 21, 23, 35, 37, 39, 41, 43, 53, 55 on ellipses and hyperbolas
Quiz on 9.5 and 9.6 (parabolas only) will be Tues. May 2