[Lecture 1, Calc I] Limits and Continuity: The Building Blocks of Calculus

What happens when a function has a hole? In this lecture, we introduce the fundamental concept of limits by filling in the gaps-literally! You'll learn how limits help us analyze functions, even at points where they misbehave, and how to determine when a function is continuous. We’ll explore right-hand and left-hand limits, tackle algebraic techniques to evaluate tricky limits, and uncover key limit theorems (without proofs, so we can stay focused on intuition). Finally, we dive into limits at infinity and their connection to horizontal and vertical asymptotes. Get ready to build a rock-solid foundation for calculus!
This lecture lays the foundation for everything to come, blending intuition and clarity to make calculus accessible and exciting. Let’s begin this mathematical adventure together!
Worksheets for this lecture are here: drive.google.c...