Calculus Fundamentals: Limits and Continuity

Feeling stuck on the first major hurdle of calculus? Limits and continuity can seem abstract, but they are the essential building blocks for everything that follows, from derivatives to integrals. This course demystifies these critical concepts. Through clear, text-based explanations and carefully selected practice problems, you will develop a deep intuition for how limits work and what it means for a function to be continuous. You'll move from basic definitions to confidently applying rules and techniques to solve a wide range of problems. What you'll learn: * Understand the formal definition of a limit and develop an intuitive feel for the concept. * Practice calculating one-sided and two-sided limits of various functions using algebraic techniques. * Learn key limit laws and how to handle indeterminate forms, including applying L'Hôpital's Rule where appropriate. * Master the definition of continuity and learn to test for it at a point and over an interval. * Identify different types of discontinuities (removable, jump, infinite) from a function's definition. * Apply fundamental theorems like the Intermediate Value Theorem to understand function properties. * Use limits to find vertical and horizontal asymptotes and analyze function behavior at infinity. The course starts with the foundational theory of limits, then progresses to calculation techniques and the concept of continuity, with plenty of examples and exercises to reinforce your learning. You will read through step-by-step solutions to build your problem-solving skills. This course is designed for absolute beginners to calculus. No prior experience with limits or continuity is required, making it ideal for high school students, university students, or anyone looking to build a solid mathematical foundation. Start building your calculus skills today.