Importance of Functions, Limits , Continuity and Differentiability
🔹 1. Functions What: A function is simply a rule that assigns each input (x) to exactly one output (f(x)). Why Important: Functions are the language of mathematics and science . Any physical quantity (distance, velocity, energy, population, etc.) is expressed as a function of time, space, or another variable. Example: Distance covered in time → s ( t ) s(t) Pressure depending on volume → P ( V ) P(V) Role: Without functions, we cannot represent relationships between variables, which means no equations of physics, no chemistry rate laws, no economics graphs. 🔹 2. Limits What: The value a function approaches as the input approaches some point. Why Important: Limits form the foundation of calculus . They allow us to define concepts like instantaneous velocity, slope at a point, and continuous change. Example: Speedometer in a car shows instantaneous speed , which is defined using a limit (distance/time interval as interval → 0). In chemistry...