Final Review for Math 126, Fall 2011

Things to be able to do:

[An absurdly short list of sample problems from the textbook related to this type of subject are given for each topic, in brackets]
  1. Larger problems (often, word problems)
    1. related rates [3.7.{7,9,19,21}]
    2. optimization problems [3.6.{1,8,9,19}]
    3. graphing [3.5.{2,3,17,18}]
    4. volumes
      1. by slices [5.2.{5,7,25}]
      2. by shells [5.3.{5,9,33}]
    5. work [5.6.{5,7,8}]
  2. Shorter (often, more computational problems)
    1. limits
      1. computing them graphically [1.2.{7,8,9,10}]
      2. computing them algebraically [1.3.{5,7,13,17}]
      3. verifying the ε-δ definition
        1. for linear functions [1.6.{1,3,5}]
        2. reading off from a graph [1.6.{15,17}]
    2. continuity
      1. recognizing [dis]continuity (three features) [1.4.{1,9,13,35,36}]
      2. using the Intermediate Value Theorem (finding roots in intervals...) [1.4.{31-34} (don't do the "bisections")]
    3. derivatives
      1. computing from the definition [2.2.{3,5,9}]
      2. computing with differentiation rules [2.5.{6,14,15,20}]
      3. writing the equation of a tangent line [2.5.{21,22},2.6.{23,25}]
      4. identifying graphs of a derivative and second derivative [2.2.{13-18},2.3.{31,32}]
      5. using Implicit Differentiation [2.7.{5,7,13}]
      6. differentiability -- identifying what can go wrong [2.2.{25,26}, 2.5.39]
      7. using linearization (the TL) to find approximate function values [3.1.{1,2,3,7}]
    4. integrals
      1. the Σ notation and Riemann Sums [4.2.9]
      2. to compute (or computing with) signed area [4.3.1,4.4.{17,24}]
      3. indefinite -- computing ADs [4.1.{7,13,33,37}]
      4. using all versions of the FTC [4.5.{7,11,13}]
      5. differentiation definite integrals with complicated limits of integration [4.5.{25-32}]
      6. using the substitution rule [4.6.{5,7,11,17}]
      7. areas between curves [5.1.{2,4,9}]
Additional bonus: A student [Darla Skolnekovich; thank you, Darla.] in our class put together many quiz, test, and important-seeming HW problems from the semester into a "practice final", which I am posting here. This was put together by a student, so I make no guarantee it is the best set of problems to use to study for the final — however, it does have many useful problems on many of the topics we covered this term. It is perhaps short a few problems on related rates (problem 85 here on the light between two buildings is probably too involved to be a good example of related rates problems which could reasonably appear on the final), on work, and on slice- and shell-method volume computations; also, the "method of bisections" mentioned for finding zeros of functions (problem 14 here), using the Intermediate Value Theorem, is something I told students not to spend time on (although the rest of that problem is quite reasonable). I did proof-read it, and it contains no typos that I have found.