Day 05 in Mat121

Today:

• Return Quiz 1
• Calculus lab
• Roll
• Directed reading handout, Section 2.3 (html) (pdf)
• Section 2.2: Limits: A Numerical and Graphical Approach
  • How do the values of a function f(x) behave when x approaches a number c, whether or not f(c) is defined?
    • Definition of a Limit
    • Important idea: as we approach c along the x-axis, what are the y values doing?
    • Theorem 1, p. 52
      • demonstration)
      • Example: #14, p. 58
    • One-sided limits: example, #33, p. 58
    • Important Cases:
      • Limit exists and equals function value

        Example: All polynomials, at every value of c!

      • Limit exists and does not equal function value
        • where function value exists; e.g. "jump discontinuity" at x=1
        • where function value does not exist
      • Limit does not exist
        • one-sided limits exist and are unequal; e.g. at x=-1

          postal rates

      • Infinite limits; e.g. at x=0

        Examples: #40, 42, p. 58

  • (from this site)
  • Questions regarding Homework/directed reading handout? Section 2.2 (html) (pdf)

• A pdf slide show demonstrating the approach of the secant lines to the tangent line.
• Function composition applet