Calculus: Chapter 1: Limit of the Function
Return to Table of Content Chapter 1: Limit of the Function The limit is the first character of any function which tells about the nature of the function. . The limit represents the value that approaches as gets arbitrarily close to from both sides (left and right). Limit is the foundation of many properties of function like continuity, differentiability etc. Limits Definition When examining a real-valued function and a real number " ," the limit is typically expressed as follows: "The limit of as x approaches c equals ." The notation "lim" denotes the limit, while the arrow signifies that the function converges to the limit as x approaches . Properties of Limit: 1. Linearity : The limit of a sum or difference of functions is the sum or difference of their limits. Sum Rule: Example : Difference Rule: Example : 2. Product Rule : The limit of a product of functions is th...