What are the three conditions for continuity at a point? Calculus Limits Definition of Continuity at a Point 1 Answer Alan P. Mar 9, 2018 A function #f(x)# is continuous at a point #(a,b)# if and only if: #f(a)# is defined; #lim_(xrarra) f(x)# is defined; and #lim_(xrarra) f(x) =b# Answer link Related questions What is continuity at a point? What is the definition of continuity at a point? What does continuous at a point mean? What makes a function continuous at a point? How do you find the points of continuity and the points of discontinuity for a function? What does continuity mean? How do you use continuity to evaluate the limit #arctan(x^2-4)/(3x^2-6x)#? How do you find the points of continuity of a function? How do you find the continuity of a function on a closed interval? If #f(x)= (x^2-9)/(x+3)# is continuous at #x= -3#, then what is #f(-3)#? See all questions in Definition of Continuity at a Point Impact of this question 40850 views around the world You can reuse this answer Creative Commons License