Limits and Continuity

Limits and Continuity

1. Continuity

   • Composites
   • Continuous Function
     • Continuous on an interval
   • Intermediate Value Theorem for Continuous Functions
     • Intermediate Value Property
     • A consequence for graphing: Connectivity
   • Algebraic Combinations
   • Continuity at a point
     • At a left endpoint a & right endpoint b
     • At an interior point c
     • Discontinuous
       • Jump discontinuity
       • Infinite discontinuity
       • Oscillating discontinuity

2. Rates of Changes and Limits

   • Properties of Limits
   • Average and Instantaneous Speed
     • Average Rate of Change
     • Instantaneous Speed
   • One-sided and Two-Sided Limits
     • Right-hand limit
     • Two-sided limit
     • Left-hand Limit
   • Definition of Limits
     • f has limit L as x approaches c
   • Sandwich Theorem

3. Rates of Changes and Tangent Lines

   • Average Rates of Change
   • Tangent to a Curve
   • Slope of a Curve
     • Tangent line to the curve
     • Difference Quotient
   • Normal to a Curve
     • Normal line
   • Speed Revisited
     • Instantaneous rate of change

4. Limits involving Infinity

   • Finite limit as x tend infinity
     • Horizontal Asymptote
   • Sandwich Theorem
   • Infinite limits as x tend a
     • Vertical Asymptote
   • End behavior Models
     • Right end behavior model
     • Left end behavior model
   • "Seeing" Limits as x tend infinity