Math 182 - Spring 2007
Calculus and Analytic Geometry II 

Last Updated: April 10, 2007.
file

Math 182 Header

rainbow

The course % will determined from 3 evening common hour midterm exams, a comprehensive final exam and quizzes and/or homework assignments. Exam dates are located below. Quiz and/or assignment due dates are determined by the section instructor and may vary from section to section. The relative weights of the exams and quizzes are also tabulated below. Exam locations depend on the section you are in. These locations will be (posted below on this web page) and announced later in your section. 

5.5  7-31 (odd numbered), 35, 41, 43, 49, 51, 55, 65, 79
5.6 4a) but only show 5/6 is less than ln(3), 10 - (Use 8 and 15)
6.1 1,3,5,9,10,13, 15, 17 (integrate in y), 21 (trig ident. for sin(2x)), 45
6.2 1,3,5,8,9,11, 13 and three harder ones: 33,35,51
6.3 3,5,7 (which curve is above?),9,11,15,19,21,23
6.4 7,9,11,21 (water's density is 1000kg/m^3) ,23 and some supplementary work problems:
 Work Problems-troughs This supplementary sheet contains some basic theory related to questions like 21 and 23 above - and --- some additional questions with solutions.
6.5 1,3,5,7,9 (Mean Value Theorem for Integrals),13,19
MIDTERM 1 See below for a description of the exam content
7.1 1-15 (odd), 19,21,23,25,27,33,35,52, 57, 59,63
7.2 1,3,5,7,11,14 (ANS=Pi/16),15-21 (odd),25,27,29,31,41,47,61
7.3 1,3,5,9,11,12 (subway?),15, 17, 19-29 (odd)
7.4 1,3a),7-15 (odd), 19, 29,39 (u=sqrt(x-1)), 41 (u=sqrt(x), 47 (u=e^x)
7.5 Mixed Integration Problems This worksheet is a set of practice problems you can do between
now and the next exam. Most of them work out with "nicer" numbers than the homework
and are more indicative of the type of integration questions that might be on the exam.
There is a chance of typos etc. so if you think there is an error, let your instructor know.
7.8 2 (a) no (b) yes (c) yes (d) yes, 5, 7, 9, 11, 15, 19-31(odd), 37,39,49,51
8.1 8.1: 3, 5,7, 8 (ANS=6+1/4*ln(2)), 10 (ANS=ln(2+sqrt(3))), 11,
y=1+2/3x^(3/2) over 0< x < 2 (ANS=2sqrt(3)-2/3), 37
8.2 1,3 and the problems a)-e) listed below:

Other problems in 8.2 are very hard integrals. 
So, try finding the surface area of the surface formed by revolving the following 
curves about the x-axis:

  • a) y=2x over 1 < x < 2 (ANS=6Pi*sqrt(5)) - frustrum of a cone
  • b) y=sqrt(x) over 0 < x < 2 (ANS=13Pi/3) - paraboloid of revolution
  • c) y=x^3 over 0 < x < 1/sqrt(3) (ANS=1/27*Pi*(2sqrt(2)-1)) -- messy but doable
  • d) y=sqrt(9-x^2) over 1 < x < 3 (ANS=12Pi) - part of a sphere
  • e) y=sin(x) over 0 < x < Pi (ANS=2*Pi*(sqrt(2)+log(1+sqrt(2))) - use integral #21 in tables
8.3 DELETED FROM SYLLABUS - WILL NOT BE ON MIDTERM 2
Improper Integral, Arclength, Surface Area Worksheet: This worksheet consists of (doable) practice problems  for improper integrals, arclength and surface area problems. 
MIDTERM 2 See below for a description of the exam content
11.1 5,7,9,11,15-21(odd), 25-33 (odd), 39, 51,55-59 (odd)
11.2 9,  15-25 (odd), 27 (consider the series as two sums and use eqn 4)
31 (Theorem 7), 33 (consider as two sums, eqn 4 and example 6)
41,43,45
11.3 3,5,7, 12 (compare with integral of f(x)=1/x^(3/2)),
13,15,17,21,25,27
11.4  3-23 (odd) using either comparison test or limit comparison test
 29 - try comparison with 1/(n*(n-1)) -- why?
 31 - try just comparison test - what is sin(x) bigger than?
11.5  For the first few questions you should either use the Alternating Series Test (AST)
 or the Test for Divergence on page 718. Since the terms in the series have signs
 which alternate you can't use comparison or integral tests - why?
 Also, you must determine the "n" for which the terms b_n are decreasing
 for - Example 3 is a good template for this.

  3,5,7,9,11 (n>1), 13 (n>2), 15, 17, 19 (what does a_n approach?)

  23, 25, 27, 32 (ANS: p>0)
11.6 Although many of the problems in this section involve using the Ratio Test (RT)
or the Root Test (RooT), you may also need to use the Divergence Test (DT),
the Alternating Series Test (AST), Integral Test (IT) or Comparison Tests (CT) to decide
whether they converge absolutely, diverge or converge conditionally. Below is
a summary sheet for all the basic theory and tests we've learned to date. I've indicated
some possible tests you can use to answer the problems in 11.6 but they may by no means
be the only ways one can answer the questions. Try to answer the problems
below without these hints first.

3,5,7,9,11,13,15,17, 21,23,31  

Hints:

 3 (RT,AST), 5 (RT,AST), 7 (DT), 9(RT), 11(CT, e^(1/n) < 3), 13 (RT),15(RT)
 17 (CT, compare with 1/n), 21 (RooT, 3^(1+3n)=3*(3^3)^n=3*(27)^n), 23 (RooT)
Here's a summary sheet of all the convergence/divergence tests. It does not include
a discussion of telescoping series though.

  Summary Sheet for Infinite Series
11.7  Are listed below under the description of Midterm 3
11.8  3,5,7,9,11
MIDTERM 3 Will cover 11.1-11.8 only (not 11.9). More details are listed below
11.9 3,5,7,9 (all are algebraic variants of the geometric series)
 13,17 (is like 13)
 15,19 (integrate an appropriate geometric series)
  21 (use a log identity first)
  20 (geometric series -GS), 18 (differentiate first to make it look like a GS)
11.10 This will NOT be on Midterm 3 but will be part of the final exam content.

3-17 (odd), 23-29 (odd), 39, 40, 47,49

Additionally, the first three nonzero terms of the Maclaurin series of the functions below:

f(x) = sqrt(1+x) = 1+x/2-1/8*x^2 + ....
f(x) = sqrt(1+x^2) = 1+1/2*x^2 -1/8*x^4 + ...
f(x) = 1/sqrt(1+2x) = 1-x+3/2*x^2 + ....
10.3  1,3,7,9,11,15,17,19,21,23,29,31,35,37  -- definitely on exam. Make sure you know how to graph polar equations.
10.1-10.2 Will NOT be on the final exam but possibly lectured on at the instructor's discretion. This material is useful to know if you plan on going on to Math 224. The 3-D version of the same stuff is done in Math 224.
10.4 REMOVED FROM SYLLABUS.
Not on final but recommended reading if you plan to take Math 224
FINAL
EXAM CONTENT IS LISTED BELOW!!!!!. Also check out the 2006 Fall Final



SUMMARY OF EXAM CONTENT FOR Spring 2007:
 OLD EXAMS AND SOLUTIONS:

EXTRA HELP RESOURSES 

  1. You can always ask your instructor about homework and course material - either in class or during their office hours. 
  2. The math department also has a tutoring center called the Math Learning Center located in Wil 1-112 - open 9am-2pm. Most tutors there should be able to help you out. The actual Math 182 instructors will be in the center: M10am,Tu1pm,W11am,Th12pm, F10am and F11am.
  3. Lastly, there are some interactive resources available through the web. As a couple of examples, you might check out the following but in the end pen and paper usually work best. Sites like these can often given one a false sense of security.

Itchy Cartoon

Campus Life