Homework Assignments

Homework is due twice a week, on Mondays and Fridays before class. Homework assigned on Monday is due on Friday; homework assigned on Wednesday is due the following Monday; and homework assigned on Friday is due the next Friday. Use the labelled homework boxes in the front (section 2) or back (section 1) of 101 Bradley (formerly Filene) Auditorium for submitting and picking up graded homework. New homework will be added below weekly.

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#0 On Wednesday, September 22, the day of the first Math 3 class:

Go to the "Maple" section of the Math 3 website and read the document "Getting started with Maple." First, follow the instructions for loading Maple onto the hard disk of your computer. Next, follow the instructions for customizing Maple for calculus, returning to the "Maple" section of the website and downloading the "Math 3 Maple files." Finally, follow the directions for trying out Maple. Only if you experience problems should you go to the Help Session on Thursday in Bradley 101, 4:00-5:00 or 5:00-6:00. Otherwise, you are ready for class on Friday.

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#1 Wednesday 9/22 (due 9/27)

• P.4 and CAS #1:
p.34 [2,4,6 (just find the domain),12,14,18,50].
In problem 50, use Maple to do the problem. Hand in both the code you write and the output showing the graph. You do not need to verify your conclusions algebraically.

#2 Friday 9/24 (due 10/1)

• P.5 and §3.1:
p.34 [40,42]
p.40 [8(c),12,17 (Use Maple if you want, but you shouldn't need to.),20,22]
p.178 [2,6,10,22 (You may assume the function in problem 10 is one-to-one without showing it.)]

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#3 Monday 9/27 (due 10/1)

• P.6:
p.53 [2,3,8,20,24,32].
Do problems 2 and 3 by drawing a suitably positioned triangle. Give exact answers to these two problems and to number 32, not just approximations.

#4 Wednesday 9/29 (due 10/4)

• §1.1:
p.59 [1,2,3,4,9,10,11].

#5 Friday 10/1 (due 10/8)

• §1.2:
p.68 [3,4,2,10,12,22,23,37,41,58]
You may use problems 3 and 4 to do part of problem 2.

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#6 Monday 10/4 (due 10/8)

• §1.3:
p.74 [2,3,6,10,12,14,20,28].
In problems 12 and 14, also sketch the graph of the given functions and all the asymptotes of the graphs. Include all relevant limits in your answers.
Also, find the limit of tan(x) as x approaches Pi/2 from the right. If the limit does not exist, is it infinity, negative infinity, or neither?

#7 Wednesday 10/6 (due 10/11)

• §1.4:
p.85 [2,7,10,16,18,29].
In problems 7 and 10, just say where the given functions are continuous and discontinuous, but be sure to give a brief explanation of your answers.

#8 Friday 10/8 (due 10/15)

• §2.1:
p.100 [3,14,15,18]

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#9 Monday 10/11 (due 10/15)

• §2.2 and CAS #2:
p.108 [2,4,6,22,26,34,36,40,41].
Also, have Maple plot the graph of both f(x) = x^3 - 3x^2 + 2x +1 and its derivative f'(x) over the same interval. Choose this interval so that the graph of f clearly shows two points with horizontal tangent lines. Hand in both the code you write and the output.

#10 Wednesday 10/13 (due 10/18)

• §§2.3, 2.4:
p.117 [2,6,12,27,32,41,45]
p.123 [2,8,14]

Note: The first Hour-Exam is a week from today. We will be posting a set of practice problems in the Study Guide section of the Math 3 website by the end of the week.

#11 Friday 10/15 (due 10/22)

• §2.5:
p.129 [14,16,20,28,30,34,37,42]

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#12 Monday 10/18 (due 10/22)

• §2.6:
p.137 [2,10,11,12,13,15].
Also, show that the function in problem 22 on page 178 has an inverse by working with its derivative.

#13 Wednesday 10/20 (due 10/25)

• §§2.8, 2.9:
p.149 [2,8,11,24]
p.154 [2,5,11,14,17]

Note: For this Friday, October 22, go to the CSC section of the Math 3 website and download CSC A-- Parts 1 and 2, CSC A: Report, and CSC A: Grading Key. Once these Maple worksheets and Word documents are on your computer, you should be sure that you can open them, and that you have browsed them enough to be familiar with what is there. We will be introducing CSC A in class on Friday. The report will be due a week from today.

#14 Friday 10/22 (special due-date, 11/1; no class Friday, 10/29)

• §2.10:
p.160 [4,8,13,15,30,34,42].

The report on CSC A will be due in class (in the homework boxes) on Wednesday, October 27.

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#15 Monday 10/25 (due 11/1)

• §2.11:
p.167 [3,4,5,8,11].

#16 Wednesday 10/27 (due 11/5)

• §§3.1, 3.2, 3.3:
p.192 [2,6,8,11,20,25,28,35,50,61 (Just determine where f is increasing and decreasing.),67]

Note: The report on CSC A (Rates of Change: Torricelli's Law) is due in class today 10/27 (in the homework boxes).

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#17 Monday 11/1 (due 11/5)

• §3.4:
p.200 [9,10,11,16,25].

Also, with reference to the material starting on page 994 of the textbook, and in CSC B, Part 2:
Let y be the solution of the IVP

y' = 1 - 2xy
y(-1) = -1
(a) By hand, use Euler's method with step size h = 1 to approximate y(3).
(b) Using the command DEtools[dfieldplot] and the Maple worksheet Class Demo: Slope Fields and Euler's Method, have Maple draw the slope field of the differential equation in the IVP above.
(c) Illustrate your work in part (a) by printing a copy of the slope field of part (b) and drawing on it the line segments that approximate the graph of y from x= -1 to x = 3.
(d) Use Euler's Method with step sizes of first h = .5 and then h = .1 to find better approximations to the graph of y from x = -1 to x = 3 by modifying and implementing the Maple code from Class Demo: Slope Fields and Euler's Method. (Note that in this worksheet you will have to change the line "numPts=100;" to get different step-sizes.

Note: For this Wednesday, November 3, go to the CSC section of the Math 3 website and download CSC B-- Parts 1 and 2, CSC B: Report, and CSC B: Grading Key. Browse these documents and worksheets enough to be familiar with what is there. We will be introducing CSC B in class on Wednesday. The report will be due next week, on Friday, November 12.

#18 Wednesday 11/3 (due 11/8)

• §3.5:
p.209 [2,3,4,5 (Also find arcsin(sin (.7 + pi)).),7,19,24,25,29,33,52]

Note: The second Hour-Exam is a week from today. We will be posting a set of practice problems in the Study Guide section of the Math 3 website by the end of the week.

#19 Friday 11/5 (due 11/12)

• §§4.2, 4.3, 4.4:
p.256 [5, Sketch the graph of y = x^3 - x using y' and y''., 8,13,30,39]

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#20 Monday 11/8 (due 11/12)

• §§5.1, 5.2, 5.3:
p.303 [1,10,18].
p.316 [1,3]

#21 Wednesday 11/10 (due 11/15)

• §§5.3, 5.4:
p.310 [16]
p.316 [14]
p.323 [1,4,8,9,11,22,37]

Note: The second Hour-Exam is today, 3:30-4:45. It covers material through class #20. Section 1 (Clark/Lahr) will take the exam in 101 Bradley, Section 2 (Kiralis) in 105 Dartmouth.

#22 Friday 11/12 (due 11/19)

• §§5.5, 5.6:
p.329 [1,2,8,12,13,19,24,25,42,44]
p.337 [4,7]

Note: The report on CSC B (Modeling with D.E.s: Population Modeling) is due in class today 11/12 (in the homework boxes).

Note: For next Monday, November 15, go to the CSC section of the Math 3 website and download CSC C-- Parts 1 and 2, CSC C: Report, and CSC C: Grading Key. Browse these documents and worksheets enough to be familiar with what is there. We will be introducing CSC C (Flooding) in class on Monday. The report will be due on Friday, November 19.

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 This week we have made some minor adjustments to the Day-by-Day syllabus to ensure that there is sufficient time to do justice to the CSC. All departures from the syllabus are noted below.

#23 Monday 11/15 (due 11/19)

• §§6.1, 6.6; omit §6.7:
p.337 [44,47]
p.351 [1,2,5,7]
p.390 [5]
Also, complete the following problem:

(a) Write out the trapezoidal approximation T5 to the integral from 0 to 1 of exp(-x^2) dx .
(b) Evaluate T5 using Maple. [Don't forget thet you will have to precede your "trapezoid(f(x),x=a..b,n);" command-line with the line "with(student):" and that you will have to use the "evalf()" command to get a decimal approximation.]
(c) Approximate the integral from 0 to 1 of exp(-x^2) dx to three decimal places by evaluating Tn using some values of n > 5.

Note: Today, CSC C (Flooding) will be introduced in class by Leslie Sonder, Professor of Earth Sciences. The report on CSC C will be due at the end of the week on Friday, November 19.

#24 Wednesday 11/17 (due 11/22)

• §5.7 (§7.1 moved to Friday):
p.342 [2,4,5,13]

#25 Friday 11/19 (Do not hand in; there is no time to grade and return the homework from now on.)

• §§7.1, 7.3:
p.415 [5a,10a,13]
p.427 [3,7,10,13]

Note: The report on CSC C (Integrals as Limits of Sums: Flooding) is due in class today 11/19 (in the homework boxes).

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#26 Monday 11/22 (Do not hand in.)

• §§7.9, 4.6:
p.428 [18,21 Do these two problems by implementing the trapezoid rule wih Maple. You may use the worksheet Class Demo: The Trapezoid Rule for this purpose.]
p.472 [1,5,6,13,22]
p.272 [1]

#27 Wednesday 11/24 (Do not hand in.)

• §§4.6, 4.7:
p.272 [3,7,8]
p.279 [1,3,7,9,15,17,19 (Just find the approximate values in the last three problems. Don't wory about the errors.)]

Note: The Registrar has scheduled the final for Sunday, December 5, 4:00-6:00 p.m. in Cook Auditorium. Practice problems for the final exam will be posted sometime on Monday, November 29.

Have a nice Thanksgiving break.

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