Dr. Barry Peratt | 204 Gildemeister Hall | 507.457.5567 (Voice) | 507.457.5376 (Fax) | bperatt@winona.edu

MATH 160---CALCULUS I 
Fall 2009

Course Materials Homepage | Math/Stat Homepage | Personal Homepage

• Study for Optional Test #2, if you are taking it. See details in Assignment 35 below.
• Section 6.1: 1-4, 6-8, 13, 15, 19, 25, 45, 49, 51.

• A Note on Upcoming Tests:
  • Optional Test #2 will be given next Thursday, 11/19/2009 and will cover the material from Assignments 30, 32 (optional material only), and 36 (to be given tomorrow in class).
  • Test #3 will be given on Tuesday, 11/24/2009, the day before Thanksgiving Break, and will cover the non-optional material from Assignments 30 on up. It will be the last test of the semester before the final exam. The last week of class we will spend working on the project.
• Section 5.1: 1, 2, 11, 13, 16.
• Section 5.2: 2, 5ab, 33, 34.
• Suppose we wish to estimate the area under the graph of y=e^{-x^2} from x=0.5 to x=3.2 using Euler's Method.
  • Compute the maximum error induced if we use n=1200 subintervals. (Answer: the error induced is +/- 0.00087611..., so if we round, we should round up because this number is supposed to tell us how big the error could possibly be. Thus, we could say that the error would be no more than 0.000877 or 0.00088 or 0.0009, for example.)
  • Determine the minimum number of subintervals needed to ensure that the estimate has an error of no more than 0.00001. (Answer: n>105,133.2, so n=105,134 will be the minimum number of subintervals needed.)
  • Use n=5 subintervals and report your answer as estimate +/- error. (Answer: the lower estimate is 0.2340825... and the upper one is 0.6546156..., so we report the estimate as the (upper + lower)/2 +/- (upper - lower)/2 = 0.444349... +/- 0.210266... = 0.444 +/- 0.211.)

Assignment 32
(11/06/2009)

[Test #2]
[Solutions]

• Section 4.9: 1-23 odd, 12, 14, 27, 28, 31, 36, 39, 40, 44. (This is Optional Test #2 material).
• Section 4.9: 49-53, 62.

• Practice on Position and Velocity Graphs Part II (remember that Part I was given in Assignment 14). Click here for the solutions.
• Practice on Position and Velocity Graphs Part III. Click here for the solutions.

Assignment 28
(10/27/2009)

[Quiz #9]
[Solutions]

• Section 4.3: 1-8, 10, 12, 15, 17, 25, 30*, 31*, 37, 40, 42, 54*, 62*.
• Section 4.6: 4, 31*.

• There will be no class tomorrow, 10/20/2009 due to University Improvement Day (only classes which meet before 3:00 PM are cancelled, and labs are not cancelled). Companion class on Wednesday will be cancelled as well as I will be out of town. So, on Thursday 10/22/2009 I will take questions on the homework and Quiz #9 will be given on Friday, 10/23/2009 (see Assignment 27 above) and will cover the material from Assignments 24-25
• Section 4.7: 2, 3, 7, 11-14, 17, 30-33, 35.

Assignment 25
(10/16/2009)

[Quiz #8]
[Solutions]

• Study for Quiz #8, which will be given on Thursday, 10/15/2009 and will cover the material from Assignments 20-23.
• Companion Students: I failed to collect your homework at the Optional Test, so you may turn in on Thursday with your quiz any assignments from Assignment 15 on which have yet to be graded.
• Section 3.10: 1-29 odd, 10, 33, 35, 36, 39, 40, 42*, 43**, 45**.

Assignment 22
(10/09/2009)

[Optional Test #1]
[Solutions]

• See the information below about Optional Test #1. For extra practice on inverse trigonometric functions, see Section 3.5: 45-54.
• Download the sheet of derivatives that I handed out in class today, if you did not receive one in class.
• Complete Section 3.5: 33-36.

• On Monday: I will take any questions you have about the Optional Test #1 material, which is the material in Assignments 15-19 and Assignments 6 (Section 2.3 computational problems only), 7, and 10. The test will be given on Tuesday, 10/06/2009.
• Section 3.1: 49, 52, 54, 58, 60, 63, 65, 66, 72-74.
• Section 3.2: 41, 44-48.
• Section 3.4: 61-63, 65, 69, 74.

Assignment 19
(10/01/2009)

[Quiz #7]
[Solutions]

• Study for Quiz #7, which will be given on Thursday, 10/01/2009 and will cover the material from Assignments 15-17.
• Complete the Practice on Logarithmic Differentiation.
• Section 3.6: 3-19 every other odd, 41-47 odd, 50*.

Assignment 16
(9/25/2009)

[Test #1]
[Solutions]

• Section 3.2: 3-31 odd.
• Section 3.3: 17, 18, 19, 1-15 odd, 23.

• Study for Test #1, which will be given on Thursday, 9/24/2009 and will cover selected material from Assignments 3-14. Click here for a guide to help you focus your studies.
• For initial practice, complete Section 3.1: 3-32 odd or every other odd.
• Pay particularly close attention to Section 3.1: 13, 27, 28, 30, 31, 35.

• Section 2.8: 1, 3-11, 35-38, 41, 43.
• Complete the Homework on Position and Velocity Graphs---Part I. Click here for the solutions.

• Continue practicing on ALEKS for the final assessment, which will be given this Thursday, 9/17/2009 from 10:55 to 11:55 AM in the library, 2nd floor, east side.
• Test #1 will be given on Tuesday, 9/22/2009.
• Handout on Interpreting Derivatives:1-4, 9, 10, 11, 13, 14-17. (Click here for the solutions.)
• Suppose that for a particular function of current I, in amps, as a function of resistance R, in ohms, we know that I(4.2)=0.35 and I'(4.2)=-0.072.
  • Identify the units on all of the numbers in the above statement.
  • If the resistance is measured to within 0.3 ohms, estimate the induced error on the current. (Answer: 0.0216 amps)
  • If we desire to maintain the current to within 0.01 amps, how closely must we monitor the resistance of the circuit? (Answer: to within 0.139 ohms)
  • Estimate the current when the resistance is 4.5 ohms. (Answer: 0.328 amps)
  • Estimate the current when the resistance is 4.0 ohms. (Answer: 0.364 amps)

• Continue practicing on ALEKS for the final assessment, which will be given this Thursday, 9/17/2009 from 10:55 to 11:55 AM in the library, 2nd floor, east side.
• Test #1 will be given on Tuesday, 9/22/2009.
• Section 2.7: 5-7, 10ab, 11-12, 14, 17, 18-21, 26-30 even, 31-33, 35, 38.

• Someone pointed out that the homework assignment last night was incorrect. The problems assigned should have come from Section 2.6 and not Section 2.8. I have corrected that in Assignnment 10 below.
• Section 2.5: 40-43, 47, 48, 51, 45, 46.
• Consider f(x)=|x³+2x²-3|/(x-1). Determine the points at which f(x) has a discontinuity and classify the discontinuities as essential jump, essential infinite, or removeable.
• Repeat the above problem with f(x)=(x-1)/|x³+2x²-3|.

Assignment 10
(9/10/2009)

[Quiz #6]
[Solutions]

• Section 2.6: 15-35 odd.
• Continue preparing for the ALEKS final assessment, which will be given next Thursday, 9/17/2009 from 10:55 to 11:55 AM in the library, 2nd floor, east side.

• Section 2.5: 2-6, 8, 9, 15, 17-19, 35, 39, 40.
• Study for Quiz #6, which will be given on Thursday, 9/10/2009 and will cover the material from Assignments 7, 8, and 9.
• If you choose to turn in your homework on Thursday, be sure to bring it to class organized, stapled, and labelled according to assignment number and with your name on it.

• Section 2.4: 1-8, 11, 12.
• Determine the tolerance on the input that will guarantee that y=e^x2-1+7x-2 is within 0.00001 of 16. (Answer: the input tolerance must be no more than 0.00000008.)
• Determine the error that will be induced in the value of y if x=0.8 +/- 0.03 and y=e^x2-1+7x-2. (Answer: the error in y will be no more than 0.245.)

Assignment 7
(9/03/2009)

[Quiz #5]
[Solutions]

• Practice on Limits: 1-24, 27, 28.
• Section 2.2: 25-32.
• If you wish, download the Flowchart for using Limit Techniques.

Assignment 6
(9/01/2009)

• Section 2.2: 1-4, 6, 8-10, 12, 13-16.
• Section 2.3: 11-29 odd, 1, 2, 10. (All of the limits in this section can be computed using the methods demonstrated in class.)
• Study for Quiz #5, which will be given on Thursday, 9/03/2009 and will cover the material from Assignments 3-6.

• Continue working on ALEKS.
• If you wish, Derive is now available for download. For those of you who are fairly familiar with computers, you may want to go ahead and install it on your machine. If that is the case, I will make it available below:
  • First, download and install Derive 5 Trial Version on your computer, noting the directory in which it is being installed.
  • Next, download and unzip these files into the same directory in which Derive 5 Trial Version was installed.

• Note: I will check with the Math/Stat secretary about the availability of TI-89s, because this is a crucial element of the class. If there are absolutely none available and no more become available, we will have to adjust for that somehow. I will keep you posted.
• Complete the Practice on Average and Instantaneous Velocity (solutions are included).
• Section 2.1: 2, 5, 7.

• Two Notes:
  • Homeworks will be collected each quiz day, for those who choose to take advantage of this offer, and the homeworks that will be collected are those covered by the quiz. Please label your homework clearly as "Assignment 3", "Assignment 4", etc.
  • Generally, except perhaps on Wednesdays during the Companion, there is no real need to bring your textbook to class.
• Homework on Euler's Method:
  • Estimate the instantaneous velocity of an object at time t=2.3s if its position is described by the function 7sin(t³+1) if we use (Delta t)=0.000053s.  Also, determine an estimate of the error in your approximation using the method discussed in class.  (Answer: dp/dt=91.6470243528 +/- 0.024292196227, and be sure that whatever calculator you are using is set to radian mode.)
  • Estimate the instantaneous velocity of an object a time t=3.7s if its position is described by the function e^{√(t+sin(t))}.  Make sure your estimate is accurate to 5 decimal places. (Answer: 0.25307)

• Quiz #4: Complete your ALEKS Initial Assessment by Friday, 8/28/2009 at midnight.
  • Your score on the Initial Assessment will not be your quiz grade. Rather, if you complete the assessment within the alloted time, you will receive a 100% on Quiz#4. Otherwise, you will receive a 0%.
  • The assesment will be given automatically by ALEKS when you register. You may log out whenever you are and ALEKS will remember where you are in the assessment process the next time you log on, so you need not take the assessment all at once. It will consist of roughly 30 questions and should take between 1 and 2 hours total to complete.
  • Keep in mind that the purpose of the assessment is to determine those areas in which you need help so that ALEKS can give you practice on that before you take your final ALEKS Requested Assessment on Thursday, September 17, 2009 from 10:55 AM to 11:55 AM.

• Download the Handout on ALEKS and read it thoroughly.
• Quiz #1: Complete the Personal Profile Survey by Tuesday, 8/25/09.  Completion of the survey counts as Quiz #1 (hence you get either a 100% or a 0% on Quiz #1).
• Quiz #2: In one box of the Personal Profile Survey, you will enter your answer to the syllabus quiz;  this will count as Quiz #2.  Your grade will be determined by the percentage of the anomalous words you find.
• Quiz #3: Purchase an ALEKS license for our class at the bookstore, and complete the registration by Wednesday, 8/26/2009 (at midnight) OR bring it to class with your laptop on Wednesday, 8/26/2009.