Foundations of Calculus: Limits, Continuity, and Differentiability by Graph

Struggling to grasp the core ideas of calculus like limits, continuity, and differentiability? Many learners find the initial abstract definitions challenging without a clear visual foundation. This course provides a foundational understanding of these critical calculus concepts by focusing on their graphical interpretation. You will develop a strong intuition for how functions behave, preparing you for more advanced mathematical studies. What you'll learn: Understand the intuitive definition of a limit and its graphical implications. Apply graphical methods to determine continuity and identify points of discontinuity for various functions. Analyze the differentiability of a function by examining its graph for smoothness and sharp turns. Interpret one-sided limits and their role in overall limit existence and continuity. Learn to identify and interpret asymptotes and their relationship to function behavior. Practice analyzing complex piecewise functions and functions involving absolute values graphically. Grasp the conceptual link between differentiability and the slope of a tangent line. The course begins with an exploration of limits through visual examples, progressing to understanding continuity as an unbroken path. It then delves into differentiability by examining the smoothness of curves, building conceptual understanding step by step. This course is designed for absolute beginners in calculus or anyone seeking a clearer, more intuitive understanding of limits, continuity, and differentiability. No prior advanced mathematical knowledge is required. Begin your journey into the foundations of calculus with a clear, graphical perspective.