Day 8, Mat128: Calculus A

• Key for the second of the section 1.4 handouts.

• Zoom

  Here's a menu of our past zooms...

• You have no new assignment, other than to prepare for our first exam.

• Reminder: I've also assigned a couple of homework problems from section 1.3, which are due today.

• Your first exam is this Wednesday; it will cover material through section 1.4: the derivative function.

• Today we're going to be reviewing for our exam. I'll use a handout for Section 1.5 as a guide to our review.
• However, let's start with any questions. Our exam will cover
  • Average velocity (and "rate of change", more generally)
  • Instantaneous velocity
  • Geometric, numeric and algebraic calculation and meaning of rates of change (slopes of secant lines; change in y over change in x)
  • Limits -- left, right, at a point
  • Limit definition of the derivative at a point
  • Indeterminate forms
  • When derivative values don't exist (graphically, algebraically)
  • Its geometric sense (slope of a tangent line)
    1. what the sign means
    2. what zero values mean (or may mean!)

  • Use of the derivative (and average rates of change) in estimation
  • The derivative function
  • Symmetry (shhh! It's a secret...)

• Read and review your text -- sections 1.1-1.4
• Review your IMath assignments.

• Old worksheets?
• Section material?
• I have a couple of comments on your first 1.4 worksheet, 1.4
  • #2 -- the line has to go through the origin -- but how do you get that slope?
  • #3 -- there should be no "h" terms in the final answer, since $h \rightarrow 0$; don't be a limit dropper (and keep it in the right place).
  • #5 and #8: symmetry
  • #9: quadratics, cubics, and Pascal's triangle.

They're a good review of several important ideas.

• Graphing the derivative function
• The Derivative as a Function