Foundational Calculus: Limits and Continuity

Limits and continuity are the building blocks of differential and integral calculus, but they often trip up new students who lack a strong theoretical foundation. This course provides a deep, text-based exploration of these essential topics, enabling you to confidently analyze functions, determine the existence of limits, identify discontinuities, and solve complex problems. What you'll learn: * Understand the formal epsilon-delta definition of limits and its practical application to formal proofs. * Apply limit laws and fundamental theorems (including the Squeeze Theorem) to accurately evaluate indeterminate forms. * Analyze different types of discontinuities (removable, jump, essential) and formally test functions for continuity. * Practice advanced techniques like L'Hôpital's Rule for solving limits involving indeterminate forms. * Configure piecewise functions and determine parameters that ensure continuity across their entire defined domain. The course begins with core terminology and intuitive concepts before moving into formal definitions and rigorous proofs. You will then apply these principles through extensive written exercises and detailed solution analysis. This course is designed for absolute beginners in calculus, high school students, or anyone needing a strong, foundational review of limits and continuity. No prior advanced mathematics knowledge is required. Start building your calculus foundation today.