Limit Definition of Derivative

The limit definition of derivatives serves as a foundational concept in calculus, providing a precise mathematical framework for understanding rates of change and instantaneous behaviors of functions. It establishes a rigorous method for determining the slope of a curve at a specific point, crucial for analyzing various phenomena in fields ranging from physics to economics. By capturing the essence of instantaneous change through the manipulation of limits, this definition lays the groundwork for more advanced calculus concepts and applications, forming the cornerstone of calculus education and its practical use in solving real-world problems.