Calculus II: B'03 - Sections B03 & B05

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Monday, December 15, 2003; 6:00 pm

For your convenience, here is the set of answers to the even-number HW problems in Sec. 8.4.

8.4:
#2: (x/3)(e^(3x)) - (1/9)(e^(3x)) + C
#4: (t/2)(e^(2t+3)) + (13/4)(e^(2t+3)) +C
#10: (3t/8)(2t+7)^(4/3) - (9/112)(2t+7)^(7/3) + C
#12: xln(7x^5) - 5x + C
#30: (2/21)x^7(x^7+1)^(3/2) - (4/105)(x^7+1)^(5/2) + C
#38: (x/150)(3x+10)^50 - (1/22,950)(3x+10)^51 + C



Saturday, December 13, 2003; 6:30 pm

Special Problem #3 - The Winners

Section B03

1. Tyson Toloczko
2. Karl Shen
3. Jessica Lam

Section B05

1. Eric Purington
2. Joshua Rothschild
3. Sarah Rich



Saturday, December 13, 2003; 2:40 pm

This is the last time in the course when you can check your HW solutions before the quiz. The answers to the even number problems (Sections 7.7. (second half), 8.1, 8.3) are:

7.7:
#38: cscx
#40: - e^x/sqrt(1 - 2*e^(2x))
#44: - 1/[x^2*sqrt(1 - x^2)]
#56: Pi/4
#58: arctan(e^x) + C

8.1:
#4: 1/3
#12: - e^(cosz) + C
#14: arcsin(x^2) + C
#22: (1/4)*arctan(x^2/2) + C
#28: (1/4)*sec(4*t - 1) + C
#34: - (1/2)*cot(2*x) - (1/2)*csc(2*x) + C
#60: Formula 55; sqrt(16 - 3*t^2) - 4*ln[abs[(4 + sqrt(16 - 3*t^2))/(sqrt(3)*t)]] + C

8.3:
#2: (3/7)*(x + Pi)^(7/3) - (3*Pi/4)*(x + Pi)^(4/3) + C
#8: (3/8)*(1 - x)^(8/3) - (3/5)*(1 - x)^(5/3) + C
#10: 8*arcsin(x/4) - (x*sqrt(16 - x^2)/2) + C
#16: (sqrt(2) - 1)*Pi^2 - ln(sqrt(2) + 1)
#18: ln|sqrt(x^2 + 4*x + 5) + x + 2| + C



Friday, December 12, 2003; 5:05 pm

This is the last time in this course when you have an opportunity to earn bonus points by solving a Special Problem.

SP #3 is a simple integration problem which requires just careful using the technique considered today in class. For all references regarding a Special Problem, see the Special Problem Rules.

Special Problem #3 (PDF)

Solutions generated by Maple, MATLAB, calculators, and other means of technology will not be considered - even if they were used only at one minor stage of the solution. Try to get as simple analytical form for the result as possible.

The deadline for your e-mail claims regarding the obtained solution is:

Saturday, December 13, 5:00 pm.

When e-mailing your solution, please use plain text option and compose your message responsibly: there should be brief, concise, but sufficient information about the major steps your made.

The solution should be presented by a winner in the next class on Monday, December 15.

Good luck!



Thursday, December 4, 2003; 7:10 pm

Now you can check your last week homework solutions: find the correct answers to the even number HW problems (Sections 7.2 - 7.5, 7.7) below.

7.2:
#2: f-1(2) = 1
#34: f-1'(3) approx. = 1/2
#36: 1/10

7.3:
#8: e^x/x
#12: e^(2*x^2 - x)*(4*x - 1)
#14: 2*e^(-1/x^2)/x^3
#18: x^2*e^(x^3*lnx)*(1 + 3*lnx)
#20: - 2*e^(1/x^2)/x^3 - 2*x/e^(x^2)
#30: e^(x^2 - 3)/2 + C

7.4:
#6: 1/128
#8: 3/4
#18: (4*x - 3)*3^(2*x^2 - 3*x)*ln3
#22: [(2*Theta - 1)/(2*sqrt(Theta^2 - Theta)]*sqrt(ln3/ln10)
#24: 10^(5*x - 1)/(5*ln10) + C
#26: 999,999/(3,000*ln10) = (approx.) 144.76
#30: 2^(e^x)*e^x*ln2 + (2^e)^x*e*ln2

7.5:
#8: about 449 million
#12: about 8.5 days

7.7:
#2: -Pi/3
#6: Pi/3
#18: approx. 0.0263



Monday, November 24, 2003; 12:10 pm

It's time to check your HW solutions. Below please find the correct answers to the even number HW problems in Sections 6.4 - 6.6, and 7.1 which will be covered by the next (4th) Quiz on Tuesday:

6.4:
#8: 17/3
#14: 2*(17*sqrt(17) - 2*sqrt(2)) #24: 50*Pi

6.5:
#6: 6561/56 inch-pounds
#8: 6 ft-lb
#18: -28,800*[4^(-0.4) - 1^(-0.4)], or, approx. 12,259 ft-lb
#22: 32 ergs

6.6:
#2: 11.25 ft from John
#14: xbar = 1/2; ybar = 11/15

7.1:
#8: x*(1 + 2*lnx)
#12: 1/sqrt(x^2 - 1)
#22: (1/4)*ln3
#26: ln(1/(x-3))



Wednesday, November 19, 2003; 6:30 pm

Special Problem #2 - The Winners

Section B03

1. Michael Blouin
2. Tyson Toloczko
3. Cody Brenneman

(4-6. Yoojin Kwak, Jessica Lam, Marianne Pickering)

Section B05

1. Shaun Mohan
2. Sarah Rich
3. Eric Purington



Tuesday, November 18, 2003; 5:45 pm

This is the announcement of Special Problem #2. The same rules are held for this one; for details, please refer to the Special Problem Rules.

This SP is about finding the area of a surface of revolution - actually, nothing really special - just a regular problem from the section's problem set.

Special Problem #2:

Section 6.4, Problem #26 (p. 300)

To get a solution to this problem, you have to appropriately compose and correctly evaluate a definite integral. Experience in similar problems could be earned from solving Problems 24, 25, 27 (Sec. 6.4) in your HW assignment.

Solutions generated by Maple, calculators, and other means of technology will not be considered - even if they were used just at a particular stage of the solution.

The deadline for your e-mail claims regarding the obtained solution is:

Wednesday, November 19, 2003, 5:30 pm.

Please compose your e-mail claims responsibly: they should be not too long and not too short, refer to major steps, and inlcude not just the answer, but also major intermediate results. No rational approximate numbers please - the problem has an exact solution.

The solution should be presented by the winner in class on Thursday, November 20.

Good luck!



Monday, November 17, 2003; 3:40 pm

The next Quiz (No 3) is coming up, so you may wish to check your HW solutions with the correct ones. Here are the answers to the even number HW problems in Sections 5.8, 6.1, and 6.2 which will be covered by this Quiz.

5.8:
#4: (8/145)(5u - Pi)^(29/8) + C
#10: (1/30)(x^3 + 5)^10 + C
#18: (3/2)sin[(z^2 + 3)^(1/3)] + C
#24: -(5/18)[tan(x^(-3) + 1)]^(6/5) + C
#38: (1/10)sin(2Pi^5)

6.1:
#4: 32/3
#8: 9/2
#10: 22/3
#18: 72

6.2:
#2: 153*Pi/5
#8: 65*Pi/4
#12: 4*Pi/3
#16: 32*Pi/3



Sunday, November 9, 2003; 4:30 pm

This is the list of the answers to the even number HW problems in the second half of Chapter 5 (Sections 5.4 - 5.7) which will be covered by Quiz #2 on Monday, November 10:

5.4:
#2: 15/4
#4: 17/4
#8: 23/2
#12: 7/6
#14: 16/3

5.5:
#4: 15.925
#10: INT[0..Pi] (sinx)^2 dx
#12: 14/3
#18: 4

5.6:
#10: 0
#14: -2x
#16: [cos(2x)]^3tan(x)
#18: 3x^2/2 - 1/2

5.7:
#10: 15
#12: sqrt(3)
#16: 2/3
#22: 8/3



Wednesday, November 5, 2003; 6:30 pm

Special Problem #1 - The Winners

Section B03

1-3. --

Section B05

1. Sarah Rich
2. Shaun Mohan
3. --


Tuesday, November 4, 2003; 5:30 pm

Here is the first Special Problem of this course.

Although this is not mandatory, it wouldn't be wise to simply ignore this opportunity and not try to earn bonus points. You may need some points by the end of the course to improve your grade, but at that time there could be the lack of such opportunities. On the other hand, if you are not a winner now, you are not a loser at all because working with the SP you get more experience in the course material and become better prepared to the tests.

The first SP is related to the supplementary geometric stuff introduced to support the concept of the Definite Integral. For all references regarding the whole procedure, see the Special Problem Rules.

Special Problem #1:

Section 5.4, Problem #24 (p. 234)

In order to get the complete and correct solution to this problem, you'll need to apply some geometry and trigonometry. Certain level of familiarity with material of Calc I (for evaluations of the limits) is also required.

Solutions generated by Maple, calculators, and other means of technology will not be considered.

The deadline for your e-mail claims regarding the obtained solution is:

Wednesday, November 5, 2003, 5:30 pm.

The solution should be presented by a winner in class next day, Thursday, November 6.

Good luck!



Sunday, November 2, 2003; 4:30 pm

When preparing to the first quiz, you may find it useful to check the results of your Homework solutions with the right ones. The odd answers are available in the text whereas the answers to the even number HW problems (Sections 5.1 - 5.3) are given below:

5.1:
#6: (9/5)x^(5/3) + C
#14: x^6/6 + x^5 - (3/4)x^4 + (sqrt(3)/3)x^3 + C
#18: x^4/4 + 1/x + C
#24: (2/7)s^(7/2) + (4/5)s^(5/2) + (2/3)s^(3/2) + C
#26: t^3/3 - 2sint + C
#30: (2/9)sqrt[(5x^3 + 3x - 2)^3] + C

5.2:
#12: u = (t^2 - (1/4)t^4 + 1/16)^(-1/2)

5.3:
#6: -1154/105
#12: SIGMA[i=1..100] (1/i)(-1)^(i+1)
#14: SIGMA[i=1..502] bSUB(2i-3)
#28: 22,825
#34: SIGMA[i=1..10] isin(Pi/i)

Please remember that the full credits will be given only to the full solutions, i.e., with all intermediate steps and shown in complete math notation. A reproduction of the correct answer on the quiz paper without the work leading to this answer will not be considered a solution deserving even a partial credit.


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Last modified: Sat, Dec 13, 2003