Math 132 - Home

# Home

Math 132, Spring 2012

#### Monday, May 14

Grades are posted, and the semester is done. I wish you the best of luck with all your future courses.
For your reference, here is the final.

#### Thursday, May 3

The answers for the multiple choice/long answer blends on the Spring 2010 final are: 1. iv, iii; 2. i, iv; 3. ii; 6. i, iii, ii; 7. ii, v.

#### Monday, April 30

As far as old exams go: the exams for Math 132 in Spring 2010 were mainly hand-graded. We've done things in enough of a different order that the midterms from that semester would not have been useful for you, but the Spring 2010 final may be of some help in your studying. (I expect this to go up on the oldexams page soon, also.)

#### Friday, April 27

Also, here are the quiz and worksheet from Tuesday.

#### Friday, April 27

My office hours for reading week are: M 4pm - 5pm, T and W 10am - 12pm, Th 11am - 2pm.
Calc help room will be open through Thursday at 2:30.

#### Monday, April 23

Webwork problem 4 had at least two problems with it. I think all the bugs should be out now.
You can do this problem either by taking derivatives directly; or else by multiplying the series for sqrt(x) and e.g. sqrt(4 - x), and finding the first few terms.

#### Wednesday, April 18

The solutions to Quiz 5 are available.

#### Tuesday, April 17

Worksheet 12 is available.

Homework hint: On #12, it might be helpful to compare with the 2nd derivative of 1/(1 - x).

#### Friday, April 13

Quiz 4 solutions, as promised.

#### Friday, April 13

The webwork due date was incorrectly set -- sorry about that. Now fixed so that hw 12 is open, and will be due this coming Wednesday.
Under these circumstances, I'd be especially inclined to grant requests for extra time, if anyone needs such.

#### Friday, April 13

Quiz 4, given today, is available. (Solutions to follow.)

#### Tuesday, April 10

As you've all seen by email:
On Exam 3, the lowest A- = 81, lowest B- = 62, lowest C- = 35.
For the record, on Exam 2, the lowest A- was 88, lowest B- was 75, lowest C- was 56. On Exam 1, the lowest A-/B-/C- were 88/76/59.

Worksheet 11 is also available.

#### Saturday, April 7

Homework hint On #15, the hard part is finding the limit of fi+1 / fi. Assume that limit L exists, and by expanding the recursion (recalling that fi+1 = fi + fi-1), set up an equation involving L. Solve!

#### Friday, April 6

The midterm grades now on WebSTAC are based purely on the grades from your first two exams, and do not include WebWork or quiz grades.

#### Thursday, April 5

Draft Exam 3 solutions are now posted. Please note that, in order to get these up as quickly as possible (before the course withdrawal deadline), I have not proofread them as closely as I usually would.

#### Thursday, April 5

Exam 3 is now posted. Solutions will follow as soon as we can.

#### Wednesday, April 4

I'll be in my office 1-3pm today to help you with any last-minute questions. My usual office hour on Thursday will be cancelled.

#### Tuesday, April 3

Worksheet 10 is now available. Good luck studying for the exam!

#### Monday, April 2

I've posted a sheet which carefully states the Domination/Direct Comparison test at vertical asymptotes.

#### Wednesday, March 28

A short WebWork is posted, to help you practice the newest material for the exam. (Due Wednesday).
Quiz 3 is also available.

#### Tuesday, March 27

Somewhat belatedly: here are solutions for exam 2.
Also, available is Worksheet 9 from today.

Another webwork hint: On #10, integration by parts sure looks like it would be helpful. (The information given is exactly what you need to "plug in" to the antiderivative.)

#### Monday, March 26

I've turned off the submission limit on #3. Please try to do it in as few submissions as possible, and generally to understand the problem.

Some hints
#4: It may be helpful to know that an antiderivative of tan2x is tan x - x. The limit (as t goes to infinity) of t ln t can be computed with l'Hopital.
#12: This problem looks scary with all the big words, but is a pretty straightforward computation, except that you have to think a little bit about s. (It's a little like the 1/xp theorem that way.) It may be helpful to see what happens with s equal to some nice values such as -1, 0, 1, 2, ...

#### Friday, March 23

Hints on WS 8 # 1d:This problem hinges on showing that the integral e.g. from 1 to 2 diverges. There are two basic approaches:
Approach A): Factor 1/(x4 - 1), and notice that the 1/(x-1) term gets big (goes to infinity) near 1, while the other two terms are around 1/2. Use this to set up a Domination Test!
Approach B): Do partial fractions on 1/(x4 - 1). You'll be able to show directly that the integral goes to infinity.

#### Friday, March 16

I hope everyone is having a relaxing and refreshing break.
We discussed differential equation, including a simple model for drug metabolization. Some of you may be interested in this article, which discusses an application of a somewhat more complicated differential equation model. This set of equations models how acetaminophen (as found in Tylenol) is cleared by and damages the liver. Acetaminophen overdoses are a common cause of acute liver failure.

#### Wednesday, March 7

Here is the Worksheet from yesterday's section.
Also, a new webwork is posted, due the Wednesday after spring break.

#### Tuesday, March 6

A pdf of Exam 2 is available. Solutions will appear later.

#### Monday, March 5

Good luck on the exam tonight!! Exam seat lookup here.
I'll have an extra office hour this afternoon 1-3pm, and will cancel my office hour on Thursday. (I'll still be available for appointments.)

#### Saturday, March 3

Ryan has written up some brief informal solutions to selected problems from Worksheets 5 and 6.

#### Friday, March 2

The new webwork is posted. Problems 1-12 are highly relevant to Monday's exam, and I highly recommend doing these problems over the weekend.

#### Thursday, March 1

The differential equation for the propofol problem (Michael Jackson problem) on the worksheet is y' = K - (ln 2)/45 y.
As usual, this is inflow - outflow. This example is essentially the same as the radioactive drip problem solved in class, and I recommend working through these two side-by-side as a good exercise.

#### Monday, February 27

The purpose of the salt/water problems on the WebWork is to give you some experience in setting up differential equations, the modeling that we spent time on last week. You should set y to be the mass of salt in the tank.

It may help to ask yourself some of the following questions:
How much salt (mass) leaves in each liter of water? (This will depend on y.) How many liters of water are leaving each minute?
How much salt (mass) is entering in each liter of water? How many liters of water are entering each minute?

#### Friday, February 24

Solutions for Quiz 2 are now posted.

#### Friday, February 24

Here's the quiz from lecture today.

#### Friday, February 24

The promised review sheet on exponential and log functions is now available, as is Worksheet 5 from section.

#### Tuesday, February 21

Note that bar(x) = My / M. (The formulas for the center of mass in class were correct, but Mx and My are backwards from what it seems they should be, and this matters for some of the webwork problems.)

#### Sunday, February 19

For the webwork, please note that the centroid of a shape is the center of mass of that shape with uniform mass density. (See p395 of your textbook for additional discussion.)

#### Friday, February 17

1. As promised, Exam 1 solutions are available.
2. The handout from today on bounding errors is also available.
3. As a bonus, I've written a solution to Webwork 4 Problem 13 (yes, that problem!).

#### Thursday, February 16

Webwork 5 is now posted.

Please note that I misstated Simpson's rule yesterday in lecture. The correct rule (as on p465 of your text) is:
S = Dx/3 ( f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn) )
where Dx is "Delta x". (The rule alternates 4's and 2's.)
You'll of course need the correct rule for your homework!

#### Wednesday, February 15

Here is Worksheet 4, with the error in 3a fixed (should be "points where slope is plus or minus 1", was "where slope is 1").

#### Tuesday, February 14

1. Physical exams are in the Math 132 cubbyholes, which are between room 112 and room 114 in Cupples I Hall. The sheets are sorted by the problem number, and it would be courteous to your fellow students to keep them that way.
2. If you have trouble finding one or more sheets of your exam, you might try looking under your first name, or in the neighboring cubbyhole. If you didn't put your name on certain sheets of your exam, then finding them again might be a difficult problem.
3. If you don't want to go out in the cold, I've "uncovered" all numbers concerning Exam 1 on Telesis.
Details on the multiple choice problems are available on mathlookup.
4. A rough scale of grades: lowest A- is around an 88. Lowest B- is roughly a 76. Lowest C- is about a 59.

#### Tuesday, February 14

Happy Valentines day!! To celebrate, some homework hints:
On 7, an antiderivative of sec x is ln(cos(x/2) + sin(x/2)) - ln(cos(x/2) - sin(x/2)).
On 13, notice that the problem is stated in terms of x instead of y, but still rotated around the x-axis. With surface areas of rotation which variable you use for the f(x) is important, so you'll need to switch variables. The algebra is daunting, but take heart -- there's lots of cancellation, and the resulting integral is not too bad. I've checked it carefully, and the webwork answer is indeed correct.

#### Wednesday, February 8

Good luck on the exam tonight!! Exam seat lookup here.
Worksheet 3 from yesterday is posted.
Reminder: my office hours tomorrow 2/9 are cancelled.

#### Monday, February 6

A mockup (link now fixed) of the exam format is available. The real exam will have 5-6 multiple choice, plus 4 long answer (each with multiple parts).
The old exams page is available if you want a real exam for practice. Fall 2011 used the same book and a similar schedule, and would not be terrible to look at.
Again, the exam covers through the material from Wednesday 2/1.
On the day of the exam you can look up your room and seat via this link.
The quiz from last week is also now posted.

#### Tuesday, January 31

The worksheet from today is now posted. Please note that 2b had an error in the hint -- the useful example to look at is Example 7 from 5.5 (rather than from 5.4).

#### Tuesday, January 31

As announced in lecture, my Thursday office hours will be cancelled.
Some old exams from Math 132 (and other classes) are archived by the math department, and may be helpful in studying for our first exam.

#### Sunday, January 29

A list of basic integrals is now posted.

#### Thursday, January 26

The webwork due next week is posted!

#### Tuesday, January 24

On problem 14 of the webwork, you want the total distance traveled, and not the displacement ("net" distance traveled). That means you'll have to split up the interval by where v is positive and v is negative, and take definite integrals with appropriate sign. (See e.g. Example 5 of Section 5.4.)

#### Tuesday, January 24

Here is Worksheet 1 from today's recitation section, including Problem 3d.

#### Thursday, January 19

The first webwork problem set is posted. Please click on the webwork link to the left.