Understanding+continuity+in+terms+of+limits

Continuity entails an output value infinitely close to the previous for every input along a specified domain interval. Testing to find values which do not exist allow one to find gap discontinuity, infinite discontinuity, or oscillating discontinuity, but not jump discontinuity with one hole.

If the limit from the left does not equal the limit from the right, then the function is not continuous. If any limit aproaches infinity or negative infinity then the function is not continuous.

As stated above, even if the limits are equal, the places where the domain is not defined can be obtained through albebraic analysis and a discontinuity found.

Example: find the type of discontinuity for the function x/IxI at x=0 Answer: the limit from the right is positive one, but the limit from the left is negative one. Since the numbers are different and not infinite, there is a jump discontinuity at x=0.