Day 12 in Mat121

Today:

• Roll
• Hand back Quiz 3
  1. Limits algebraically
     1. • choose appropriate conjugate
        • don't multiply out the (x-2)*conjugate
        • don't be a limit dropper!
        • 2*sqrt(2) is best....
     2. • expand is the trick!
        • Expand properly...
        • Non-linear functions
        • watch the weird cancellations
        • only products can be cancelled top and bottom, not sums or differences
     3. • Not indeterminate!

  2. The limit at a particular value of x is a function value, or a value along the y-axis (not the x value)

• Test Tomorrow, over chapters 1 and 2

• "Last minute" questions over material from chapters 1 and 2?

• Section 3.1: The Definition of the Derivative
  • "time, position, velocity"
    • If we have the record of the position, could we recover the velocity?
    • If we have the record of the velocity, could we recover the position?

  • Secant lines approximating tangent lines....

  • The definition:

  • Example problems:
    • #5, p. 103
    • #21, p. 104
    • #26, p. 104
    • #49, p. 105

  • Questions over the directed reading handout, Section 3.1 (html) (pdf)?