Calculus I

1
Calculus I
Chapter 2
Limits and Rates of Change
2
Sec. 2.1

• Tangent Line vs. Secant Line
• Average Velocity distance traveled
• time elapsed
• Instantaneous Velocity velocity at a specific
  instance, the limiting value of the average
  velocities over shorter and shorter time
  intervals.

3
Sec. 2.2- Limit of a function

• One-sided limits
• Infinite limits
• Vertical asymptotes

4
Sec. 2.3

• Limit laws
• Complex fractions
• Absolute value expressions
• Greatest integer functions
• Factoring
• Difference of squares
• Difference of cubes
• Sum of cubes
• Trinomials

5
Sec. 2.5 - Continuity

• 3-part definition of continuity
• f(a) is defined
• The Intermediate Value Theorem
• If f is continuous on the closed interval ,
  a,b ,and there is some number (n) between f(a)
  and f(b) then there must be a number (lets call
  it c) such that f(c)n.

6
Sec. 2.6

• Slope of secant line vs. slope of tangent line
• Average velocity vs. instantaneous velocity
• Equations of tangent lines
• Solving velocity problems, given position
  equations.