What is the definition of continuity at a point? Calculus Limits Definition of Continuity at a Point 1 Answer Wataru Oct 8, 2014 Definition A function #f(x)# is said to be continuous at #a# if #lim_{x to a}f(x)=f(a)#. I hope that this was helpful. Answer link Related questions What are the three conditions for continuity at a point? What is 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 4681 views around the world You can reuse this answer Creative Commons License