Final Review for Math 126, Spring 2010

Things to be able to do:

1. Larger problems (often, word problems)
   1. related rates
   2. optimization problems
   3. graphing
   4. volumes
      1. by slices
      2. by shells
   5. work
2. Shorter (often, more computational problems)
   1. limits
      1. computing them graphically
      2. computing them algebraically
      3. using the Limit Laws
      4. verifying the ε-δ definition
         1. for linear functions
         2. reading off from a graph
   2. continuity
      1. recognizing [dis]continuity (three features)
      2. using the Intermediate Value Theorem (finding roots in intervals...)
   3. derivatives
      1. computing from the definition
      2. computing with differentiation rules
      3. writing the equation of a tangent line
      4. identifying graphs of a derivative and second derivative
      5. using Implicit Differentiation
      6. differentiability -- identifying what can go wrong
      7. using linearization (the TL) to find approximate function values
   4. integrals
      1. to compute (or computing with) signed area
      2. indefinite -- computing ADs
      3. using FTC I, FTC II, NCT
      4. differentiation definite integrals with complicated limits of integrtion
      5. using the substitution rule
      6. areas between curves