C2: Limits & Continuity

C2: Limits & Continuity

1. 1: The Limit at a finite point

   • 1.1: Intuitive Definition
   • 1.2: Formal Definition
   • 1.3: Examples of Basic Limits
   • 1.4: Uniqueness
   • 1.5: One-sided Limits

2. 2: Infinite Limits & Limits at Infinity

   • 2.1: Vertical Asymptotes
   • 2.2: Horizontal/slant Asymptotes
   • 2.3:Examples
   • 2.4: Formal Definition

3. 3: Limit Theorems

   • 3.1: Three basic rules
   • 3.2: The Composition rule
   • 3.3: Algebraic Limits
     • Direct Substitution property

4. 4: Other Limit Properties

   • 4.1: The Cancellation Theorem
   • 4.2: Basic Limits at Infinity
   • 4.3: The (Squeeze) Sandwich Theorem

5. 5: Quotient Functions

   • 5.1: Limit Forms
     • Vertical Asymptotes & Infinite Limits
     • Horizontal Asymptotes & Zero Limits
   • 5.2: Indeterminate Limit Forms
   • 5.3: The Exponential Number e
   • 5.4: A Special Trigonometric Limit

6. 6: Continuity

   • 6.1: Basics
   • 6.2: Discontinuities
   • 6.3: Continuity on Intervals
   • 6.4: Piecewise-Defined Functions
   • 6.5: The Heaviside Function
   • 6.6: The Characteristic (Indicator) Function
   • 6.7: The Continuity Theorems
   • 6.8: Continuity of Functions
     • Algebraic
     • Exponential
     • Trigonometric
   • 6.9: Extreme & Indeterminate Value Theorems
   • 6.91: Monotonic and Inverse Functions