Calculus Fundamentals: Limits, Continuity, and Differentiability for JEE

Calculus forms the backbone of engineering mathematics, yet many students struggle with its abstract concepts. Building a strong intuitive and analytical grasp of limits, continuity, and differentiability is the key to scoring high. This text-based course guides you from foundational mathematical definitions to the systematic techniques required to solve complex calculus problems. You will learn how to analyze functions, evaluate limits, and verify differentiability with absolute clarity. Through this course, you will: 1. Understand foundational concepts of limits, including left-hand and right-hand limits. 2. Apply standard evaluation methods such as factorization, rationalization, and L'Hôpital's Rule. 3. Analyze the continuity of various functions using formal mathematical definitions. 4. Determine differentiability and locate points where derivatives do not exist. 5. Practice step-by-step problem-solving strategies tailored for competitive exam patterns. 6. Master key theorems including the Intermediate Value Theorem and Mean Value Theorems. We begin with basic definitions and terminology before moving on to rigorous algebraic methods. Each section focuses on reading detailed explanations and working through structured mathematical exercises to build your confidence. This course is designed for high school students and engineering aspirants preparing for competitive exams like the JEE. No advanced prior calculus knowledge is required, though a basic understanding of algebra and functions is helpful. Start reading today to build a flawless foundation in calculus and elevate your exam preparation.