I.Q. 1 3.1. Continuity from the Right at a Point: A function f:XR is said to be right-continuous or continuous form the right at a point x, ex if the right hand limit of f exists at x, and equal to f(x) i.e., lim f(x) = f(x). 3.2. Continuity from the Left at a Point: A function f:XR is said to be Left-continuous or continuous form the Left at a point x, ex if the Left hand limit of f exists at x, and equal to f(x) i.e., lim f(x)= f(x). 4: Continuous Function: DELI A function f:XR is said to be continuous on X if and only if f is continuous at each point of X. Example 1: Show that the function f(x) = is not continuous at x=0. Solution: Given function is f(x) = since f(x) is not defined for x=0, therefore it cannot be continuous at x=0. Moreover, we know that lim f(x)=lim- does not exist in R. Hence f(x) is not continuous at x=0. Value Addition: Note If the limit of a function f:XR does not exist at a point x, eX in R, then the function f:X-R cannot be continuous at x.