BC Calculus II, Fall 2011

Below you will find the daily homework assignments as well as various other useful items. Visit this page whenever you miss class! (Not that you ever will....)

For previous semester's quizzes and exams, please visit my Fall 2008 website. (Please forgive the format – the site is three years old.)

• [1] Thursday, 18 Aug: Here is the assessment plan for the semester. Download the BC1 review. Do as many problems as you think necessary so that you can finish by Monday. Plan ahead!


• [2] Friday, 19 Aug: Finish the review for Monday. Remember: although you may remember how to do a problem, take some to think about why a particular problem is solved a certain way. Try not to just know the method, but understand it.
  
  Dr. Fogel has generously provided solutions to the review.

• [3] Monday, 22 Aug: L'Hopital's rule practice in Section 4.2: #55-92. Good conceptual problems are #83-86. Here are more problems to test your understanding. Some additional problems for the enthusiast.


• [4] Tuesday, 23 Aug: You should finish the first set of "more problems" (#2-12) from Monday.


• [5] Thursday, 25 Aug: Recall from BC1: here is an introductory web site on solving optimization problems. Here are some more optimization practice problems.
  
  Revised steps for solving optimization problems:
  • Read the problem carefully.
  • Draw a sketch (as appropriate).
  • Define your variables.
  • Create constraint/optimization equations.
  • If necessary, reduce the optimization equation to one variable. Clearly state, in interval notation, the domain of this variable.
  • Differentiate, finding the stationary points.
  • Use the EVT/examine the second derivative as appropriate.
  
  
  To hand in on Friday: #87 on p. 233, and #13 on the second handout on the website: $$\lim_{x\to0^+}(1+2x)^{-3/x}.$$
• [6] Friday, 26 Aug: Here are some problems to do from the supplementary handout on optimization: #5, 10, 13, 14, 19, 24, 26. Do #5, 10, 13, 14, and 19 for Monday.

• [7] Monday, 29 Aug: Here is your first Homework Assignment. For those who have seen hyperbolic trigonometry in class with me before: an optimization problem. For those who have not: introduction to hyperbolic trigonometry.
  
  Do optimization problems #24 and #26 for tomorrow. Also, there will be time for some questions for Thursday's FunDay. Relevant problems from the review: #1-5, 11, 18, 19, 22, 24, 26, 29. Also, L'Hopital's Rule will be on the exam.


• [8] Tuesday, 30 Aug: Don't forget the FunDay on Thursday! Meet in the Math Study Area, please. Also, be sure to check sample exams from BC1 for the format of the exam.


• [9] Thursday, 1 Sept: Download a copy of the first FunDay. Please note that I do not post solutions. If you make test corrections or continue to work on conceptual problems, please keep them organized in a separate section of your notebook so I can look at them later on in the semester.
  
  Keep practicing optimization problems!


• [10] Friday, 2 Sept: Work problems #11-16, 26-29, and 35-40 on p. 279. Here are some VT practive problems. These problems are the type you would see on the conceptual part of a FunDay.

• [11] Tuesday, 6 Sept: Here are the problems from Section 4.9: pp. 287–8, #8–13, 20–23.


• [12] Wednesday, 7 Sept: Finish the handout we started in class, as well as any unfinished problems from the previous two sections.


• [13] Thursday, 8 Sept: Do Problems #1–5 on Newton's method, p. 261. Here is a nice Newton's method applet.


• [14] Friday, 9 Sept: Also do #9, 21, 22 on p. 262. Finish the parameterization handout for Monday.

• [15] Monday, 12 Sept: Here is a copy of the parameterizations worksheet. Also, good problems to do in the text are #12 and 21.
  
  For tomorrow, finish the homework from the weekend (to hand in), as well as up to 2(g) on today's work (maybe to hand in). Also, bring in questions you might have in preparation for the FunDay on Thursday!


• [16] Tuesday, 13 Sept: FunDay 2 on Thursday. Topics: optimization, EVT, IVT, MVT, and Newton's method. Meet in the Math Study Area.


• [17] Thursday, 15 Sept: Download the exam on optimization, EVT, IVT, MVT, and Newton's method.


• [18] Friday, 16 Sept: Download the parameterization problem. Hand this in on Monday.
  
  Here are some good related rates problems to try: #5, 7, 9, 11, 13, 19, 23, 27, and 29.

• [19] Monday, 19 Sept: Keep working on related rates. Make sure all the previously assigned problems (from Friday) are completed by Thursday.


• [20] Tuesday, 20 Sept: Finish Problems #3-20 in Section 5.2. Be prepared for a homework check on Thursday, and perhaps a random unannounced book check!


• [21] Thursday, 22 Sept: Finish the related rates problems you didn't get. Also, complete the problems assigned in Section 5.1: 37-59, odds.


• [22] Friday, 23 Sept: Things left for you to do: (1) Read Sections 5.1 and 5.2; (2) Do problems 39–50 (all) in Section 5.2; (3) Finish related rates problems; (4) Thoroughly read the curvature assignment.

• [23] Monday, 26 Sept: Finish the problem given in class: $$\int_0^3(x^3-x)\,dx.$$ Also, #19–29, odds on p. 330. Don't forget to look at the Web Resources page for review problems.
  
  Don't forget: the osculating circle project is due next Monday. Don't wait until the last minute!


• [24] Tuesday, 27 Sept: FunDay Thursday!


• [25] Thursday, 29 Sept: Work on the assignment and bring questions Friday. Don't wait until the last minute!


• [26] Friday, 30 Sept: Continue working on the homework. Don't forget to evaluate $$\int_{-2}^3(2x+x^3)\,dx$$ using limits. Problems from the book: p. 330, #33-42, 49.

• [27] Monday, 3 Oct: Homework due Tuesday: osculating circles and a Riemann sum.


• [28] Tuesday, 4 Oct: Practice the following substitution problems: #28, 37, 38, 41, and 50.


• [29] Thursday, 6 Oct: Here is the prompt for writing your original problem. Enjoy! Note the due date: many recent assignments were late. There is a 25% penalty if this assignment is late.
  

• [30] Tuesday, 11 Oct: Be prepared for an informal notebook check Thursday.


• [32] Thursday, 13 Oct: Continue work on using integral tables. No class Friday.


• [33] Friday, 14 Oct: Remember: Original Problem due Monday! There is a 25% late penalty! Problems are due by 4:15.

• [34] Monday, 17 Oct: Don't forget the Original Problem! And practice substitution, of course.


• [35] Tuesday, 18 Oct: FunDay on substitution on Thursday!


• [36] Thursday, 20 Oct: If you see a 0 for the Riemann sums assignment on PowerSchool, you may get the points back by using Riemann sums to evaluate $$\int_{-3}^5(x^4-x^2+x)\,dx.$$ This must be turned in by Monday at 4:15.


• [37] Friday, 21 Oct: CLASS CANCELLED.

• [38] Monday, 24 Oct: NO CLASS.


• [39] Tuesday, 25 Oct: Here is the Mathematica notebook for writing a basic Riemann sum. (Note: Download to your Desktop first, then open with Mathematica.) Finish Page 2 of the handout for Thursday.


• [40] Thursday, 27 Oct: Finish the packet. Hand this problem in tomorrow (no integral tables!): $$\int\frac{dx}{\sqrt{1-x-x^2}}.$$
  
  Here is the Mathematica notebook we used today for approximations. (Note: Download to your Desktop first, then open with Mathematica.)


• [41] Friday, 28 Oct: Here is the Mathematica notebook we used today for Simpson's formula. (Note: Download to your Desktop first, then open with Mathematica.)
  
  Homework for Monday: First, by completing the square and using integral tables, find $$\int\dfrac{dx}{3x^2-8x+2}.$$ Second, by adapting the Mathematica notebook, approximate $$\int_1^4(x^2+5\cos(x))\,dx$$ by using Simpson's formula with 5, 10, 20, 40, 100, 1000, 10,000, and 100,000 subintervals. (Note: this is the same function we used on the worksheet, and so you can see how quickly the values converge as compared to the other approximations.) It may be helpful to look at yesterday's Mathematica notebook for a simpler way to do this.

• [42] Monday, 31 Oct: Finish the Simpson's formula approximation for tomorrow. See how far you need to go to get an accuracy of 13.0086. Also, here's another integral for you to enjoy!
  
  $$\int\dfrac{dx}{3x^2-8x+6}.$$ And maybe do a few integration by parts problems?


• [43] Tuesday, 1 Nov: Read Section 8.1. Practice #9-14 as needed. You should be able to do #37-58, so start practicing those. There is an Original Problem due Friday, November 11. Start early! (Some of you needed to last time.) Also: $$\int\frac{dx}{\sqrt{1-x-2x^2}}.$$


• [44] Thursday, 3 Nov: FunDay tomorrow! And work on your Original Problem over the weekend.
  
  
• [45] Friday, 4 Nov: Remember, work on your Original Problem! (Your Original Problem, that is.)
  
  Those of you missing a "completing the square" problem, please hand in the one from Day 43.
  
  Here is the FunDay on Riemann sums.

• [46] Monday, 7 Nov: Problems from the book: p. 363, #27-33, 39, 41.. Also, here's an integration by parts to practice: $$\int e^x\cos(x)\,dx.$$ (Hint: You will need to perform integration by parts twice and solve for the original integral.)


• [47] Tuesday, 8 Nov: Finish up to (and including) #5 on page 2 of the packet. Also, here's a great integral to try: $$\int x\ \text {arccosh}(x)\,dx.$$


• [48] Thursday, 10 Nov: Book problems for Monday: p. 475, #17, 18, 31-42. (Note: Check the evens with technology!) Here's a great (and possible!) integral to try: $$\int \text {arccosh}(x)\,dx.$$
  
  Also, bring PlayDay ideas tomorrow! You CANNOT do homework, but may explore any calculus related topic. If you do not have a topic, I will give you one....
  
  Original Problems due by 4:15 (hard copy), 11:59 p.m. Saturday (turnitin.com).


• [49] Friday, 11 Nov: Need an idea? Here's one!
  
  See Thursday's post for Monday's homework.

• [50] Monday, 14 Nov: The integrals you should know....
  
  Here are some area problems to practice: p. 421, #13-36. Remember, doing problems both ways corroborates your answers.


• [51] Tuesday, 15 Nov: Work on problems #39-53 on pp. 421-422.


• [52] Thursday, 17 Nov: Homework problems: #27 and #31 on p. 482.. You might want to look at some examples in the book for guidance.
  
  Here is a partial fractions problem: $$\int\frac{x^5}{x(x-1)(x^2+1)}\,dx$$


• [53] Friday, 18 Nov: This Mathematica notebook might help with partial fractions.

• [54] Monday, 21 Nov: FunDay on Riemann sums, integration by parts, and partial fractions today! Practice a few areas and/or arc length problems.


• [55] Tuesday, 22 Nov:

• [56] Monday, 28 Nov: Finish the integrals we started today on trigonometric substitution.


• [57] Tuesday, 29 Nov: More practice on integrating powers of trigonometric functions.
Practice! We'll take questions on Thursday.


• [58] Thursday, 1 Dec: Work Problems #13, 17 on page 429.


• [59] Friday, 2 Dec:

• [60] Monday, 5 Dec: Happy Dodecahedron Day!


• [61] Tuesday, 6 Dec: You will be given these formulas on the FunDay: $$\sin(2\theta)=2\sin(\theta)\cos(\theta),$$ $$\sinh^2(u)=\frac12(\cosh(2u)-1),$$ $$\cosh^2(u)=\frac12(\cosh(2u)+1).$$ It looked like a very long exam, so I'm making the problem on solids of revolution Extra Credit!!


• [62] Thursday, 8 Dec:


• [63] Friday, 9 Dec: Here are some hints for the TakeHome. (Purists or those otherwise offended will not wish to read them.)
  
  Work #11, 13, 15, and 17 on p. 429 using the method of cylindrical shells (which we discussed today). Note that you should still get the same answers as those in the back of the book.