Concept
(1)
In order for a function to be continuous at a certain point, three conditions must be met: (1) that the point is in the domain of the function, (2) that the two-sided limit of the function as it approaches the point does in fact exist and (3) the value of the function equals the limit that it approaches. The continuity of a function only exists if these three conditions are met.
Sample Problems
(3)
Need help with "Continuity" problems? Watch expert teachers solve similar problems to develop your skills.
Problem 1
How to show that a function is discontinuous at a point x=a because it is not defined at a. Explanation of continuity.
Problem 2
How to show that a function is discontinuous at a point x=a because the limit as x approaches a does not exist. Explanation of continuity.
Problem 3
How to show that a function is discontinuous at a point x=a because its limit and its value at x=a are different. Explanation of continuity.
