Calculus Fundamentals: Limits, Continuity, and Differentiability

Mastering calculus is the key to scoring high in competitive engineering entrance exams, yet many struggle with the transition from basic algebra to rigorous limits. This text-based course demystifies the core pillars of calculus—limits, continuity, and differentiability—by breaking down complex mathematical theories into clear, digestible explanations. You will progress from foundational definitions to solving complex exam-style problems. Through step-by-step written walkthroughs, you will develop a deep intuitive understanding of how functions behave, when they are continuous, and how to rigorously test for differentiability. What you'll learn: - Understand the fundamental concepts of limits, including one-sided limits and indeterminate forms - Apply standard limit evaluation techniques such as factoring, rationalization, and L'Hôpital's Rule - Analyze functions for continuity across different intervals and identify points of discontinuity - Master the formal definition of differentiability and its relationship with continuity - Practice solving advanced calculus problems designed for competitive engineering exams - Develop systematic problem-solving frameworks to tackle complex mathematical proofs and calculations The course begins with essential terminology and the basic behavior of functions before moving into rigorous proofs, limit theorems, and differentiability tests. Each module features detailed written explanations and structured practice exercises to reinforce your learning. This course is designed for high school students, engineering aspirants, and beginners looking for a solid mathematical foundation in calculus. No advanced prior calculus knowledge is required, though a basic understanding of algebra and trigonometry is helpful. Start reading today to build a flawless foundation in calculus and ace your exams.