Notes, Explanations, and Examples

Study Aids

• Limits proved and used
• Derivatives proved and used

Illustrations from Lessons

• Limits
• Why are epsilon and delta used? Use the animation to determine how much the archer can deviate from the desired angle and stay within the allowed error (inner circle) on the target.
• The Illustrated Limit Definition
  • Symbolic finite (verbal)
  • Geometric finite (visual)
  • Symbolic infinite (verbal)
    
• What are epsilon and delta on a graph?  Interactive Animation or Video Example
• Demonstrate the limit of a sum of functions
• Proof of limits and continuity
• Why are they indeterminate? (Requires the Mathematica Player)
• Infinity/Infinity
• Infinity times zero
• Infinity minus infinity
• One to infinity
• Derivatives
• Why are the derivatives of x^2 and 2^x different?
• Integrals
• The Illustrated Integral
• The Meaning of an Integral
• Calculating area using rectangles
• How do I integrate an absolute value?

Examples for Assignments

• Limits
• How do I find epsilon and delta on a graph?  Interactive Animation or Video Example
• How do I prove a limit using the definition?
• Finite limit
• Infinite limit
• One sided limit
• Complicated quadratic
• Complicated substitution
  
• How do I calculate a limit using the known forms and algebraic properties?
• Video
• How do I handle other types of limits?
  
• How do I use infinite limit forms?
  
• Limits and Function Composition: Example
• Using the squeeze theorem
  
• Derivatives
• How do I prove a derivative using the definition?
• Simple function
• Complicated function

Demonstrations

• Rolle's Theorem
• Mean Value Theorem
• Exploring Concavity