Calculus II: A'99 - Section A02 & A03

N e w s

INFO - NEWS




Wednesday, October 13, 1999; 6:35 pm

This is the last web service for you - the answers to the even sample numbers.

7.1:
#10: - (1/x^3) - 3*(lnx)^2/x
#12: 1/sqrt(x^2 - 1)

7.5:
#14: 5565 years ago

7.9:
#10: 3/sqrt(3*x - 9*x^2)
#14: (6*x^2 - 4)/(2*x^3 - 4*x + 5)
#38: about 66.44 years

8.1:
#42: - (1/2)*e^(-t^2 - 2*t - 5) + C
#46: (5/2)*arcsin(2*x/3) + C
#48: (1/2)*arcsec(2*t) + C
#62: Formula #18: - (1/2*sqrt(55))*ln(abs[(sqrt(5)*x + sqrt(11)))/(sqrt(5)*x - sqrt(11)))] + C

8.3:
#12: x/(4*sqrt(x^2 + 4)) + C

8.4:
#44: (1/2)*x^4*e(x^2) - x^2*e^(x^2) + e^(x^2) + C
#50: -r^2*cosr + 2*r*sinr + 2*cosr + C

GOOD LUCK WITH YOUR FINAL!





Sunday, October 10, 1999; 1:45 pm

You can check your homework solutions last time in the course before the last quiz. The answers to the even number HW problems (Sections 7.7, 8.1, 8.3, 8.4) are:

7.7:
#6: e^x(cosx + sinx)
#12: - e^x/sqrt(1 - e^(2*x))
#18: - 1/(x^2*sqrt(1 - x^2))
#24: (1/4)*[sin(2*x)]^2 + C
#34: Pi/4
#36: arctan(e^x) + C

8.1:
#4: -(1/3)*(1 - x^2)^3/2 + C
#12: - e^(cosz) + C
#14: arcsin(x^2) + C
#20: e^[(sinTheta)^2] + C
#24: (1/4)*arctan(x^2/2) + C
#28: (2 - 2^(sqrt(3)/2))/ln2
#30: (1/4)*sec(4*t - 1) + C
#38: - (1/2)*cot(2*x) - (1/2)*csc(2*x) + C
#64: 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(17) - sqrt(41)
#18: (sqrt(2) - 1)*Pi^2 - ln(sqrt(2) + 1)

8.4:
#2: (1/3)*x*e^(3*x) - (1/9)*e^(3*x) + C
#4: (t/2)*e^(2*t + 3) + (13/4)*e^(2*t + 3) + C





Sunday, October 3, 1999; 10:25 pm

You can check your last week homework solutions now. Find the correct answers to the even number HW problems (Sections 7.3 - 7.6) below:

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: 690 million
#12: about 8.53 days

7.6:
#6: Pi/3
#18: approx. 1.957
#38: 2*x/(1 - x^2)
#40: 1/(2*x^2 - 1)





Tuesday, September 28, 1999; 4:05 pm

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

SP #3 is about differentiation of general exponential functions, but it also requires some dealing with logarithmic functions. For all references regarding a Special Problem, see the Special Problem Rules.

Special Problem #3:

Section 7.4, Problem #43 (p. 371)

Solution to this problem will be considered complete when you provide the answers to all three questions. Certain level of familiarity with the material of Section 7.4 would be of help.

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

Wednesday, September 29, 5:30 pm.

The solution should be presented by a winner in class next day, Thursday, September 30.





Friday, September 24, 1999; 6:20 pm

Now it's time to check your homework solutions again. Find the correct answers to the even number HW problems (Sections 6.6, 7.1, 7.2) below:

6.6:
#2: 11.25
#14: m = 52/3; Mx = -574-15; xbar = 0; ybar = Mx/m = -287/130

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

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





Sunday, September 19, 1999; 12:30 am

The third quiz is approaching, so check your homework solutions with the correct ones. Below find the answers to the even number HW problems (Sections 6.1, 6.2, 6.4, 6.5):

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

6.4:
#4: 17/3
#10: 2*(17*sqrt(17) - 2*sqrt(s))
#20: 50*Pi

6.5:
#6: 6561/28
#8: 6 ft.pound
#22: 32 ergs





Tuesday, Sept 14, 1999; 5:00 pm

This is the announcement of the Special Problem #2. No rule has been changed for this Problem; for any details, take a look at the Special Problem Rules.

This Problem is about a solid of revolution and its volume; the relevant procedure of finding such volumes was introduced in today's class. Only the steps discussed and illustrated there are required for getting the answer to this (in fact, very simple) SP #2. However, some experience earned by working with the problems of the regular HW assignment would be of help.

Special Problem #2:

Section 6.2, Problem #30 (p. 312)

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

Wednesday, Sept 15, 5:00 pm

The solution should be presented by a winner in class next day, Thursday, Sept 16.

Good luck! Don't miss the chance to earn several bonus points for your final grade!





Sunday, September 12, 1999; 11:55 pm

Check your homework solutions with the correct ones before the second quiz. The answers to the even number HW problems (Sections 5.1 - 5.5) are:

5.6:
#10: 15
#12: sqrt(3)
#16: 2/3
#22: 8/3

5.7:
#10: Pi
#14: [cos(2x)]^3[tan(x)]
#16: (3/2)x^2 - 1/2
#18: (2x+1)(2x^2+2x+sin(x^2+x))^(1/2)

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: 1/6





Thursday, September 2, 1999; 2:45 pm

When preparing to the first quiz, it might be useful to check your homework solutions with the correct ones. The odd answers are available in the text whereas answers to the even number HW problems (Sections 5.1 - 5.5) 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
#50: x/2 - sin2x/4 + 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)

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





Tuesday, August 31, 1999; 5:00 pm

The first news which deserves to be mentioned in the News Section is the Special Problem #1, an excellent chance to earn bonus points. Do not ignore this chance in the beginning of the term! 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.

The first SP relates to the supplementary geometric stuff required for the introduction of the concept of the Definite Integral. For all references regarding a Special Problem, see the Special Problem Rules.

Special Problem #1:

Section 5.4, Problem #24 (p. 261)

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

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

Wednesday, September 1, 6:00 pm.

The solution should be presented by a winner in class next day, Thursday, September 2.






Tuesday, October 29, 2002; 5:00 pm

Here is the first Special Problem of this course. Although this is not mandatory, it would not be wise to completely ignore this opportunity by not trying 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 mateiral and become better prepared to 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, October 30, 2002, 5:00 pm.

The solution should be presented by a winner in class next day, Thursday, October 31.

Good luck!




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Last modified: Wed, Oct 13, 1998