What Will You Learn?

• Definition of Continuity: You will understand what it means for a function to be continuous at a point and over an interval. You'll learn the formal epsilon-delta definition of continuity and how it relates to the behaviour of functions.
• Types of Discontinuities: You'll explore different types of discontinuities, such as jump discontinuities, removable discontinuities, and essential discontinuities. Understanding these discontinuities is crucial for analyzing functions.
• Determining Continuity: You'll learn techniques for determining if a function is continuous at a given point or over an interval. This involves checking limits and the existence of the function at specific points.
• Intermediate Value Theorem: You'll explore the Intermediate Value Theorem, which states that a continuous function on a closed interval takes on every value between the values it assumes at the endpoints of that interval.
• Algebraic Properties of Continuous Functions: You will study how arithmetic operations, combinations, and compositions of continuous functions result in continuous functions. This is essential for manipulating functions in problem-solving.
• Problem-Solving Skills: Through practice and problem-solving exercises, you'll develop the ability to apply the concepts of continuity to solve a wide range of mathematical problems.