What does continuity mean? Calculus Limits Definition of Continuity at a Point 1 Answer Antoine · Jim H Mar 30, 2015 In general, for a function #f# to be continuous at a point where #x = a# means that as values of #x# get close to #a#, the values of #f(x)# get close to #f(a)#. Mathematically put, #lim_(x ->a)f(x) = f(a)# check this out: Click Answer link Related questions What are the three conditions for continuity at a point? 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? 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 3593 views around the world You can reuse this answer Creative Commons License