Final Review for Math 126, Fall 2009

Things to be able to do:

1. Larger problems (often, word problems) -- for Thursday's 1.5 hour test
   1. related rates
   2. optimization problems
   3. graphing
   4. volumes
      1. by slices
      2. by shells
   5. work
2. Shorter (often, more computational problems) -- for Friday's longer test
   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