epäjatkeisuudet

Epäjatkeisuudet, in the context of mathematics, refer to points where a function is not continuous. A function is considered continuous at a point if its graph can be drawn without lifting the pen. If there is a break, a jump, or a hole at a particular point, then the function exhibits an epäjatkeisuus at that point. There are several types of discontinuities. Removable discontinuities occur when a function has a hole, which can often be "removed" by redefining the function at that single point. Jump discontinuities happen when the limit of the function from the left does not equal the limit from the right. In these cases, the graph abruptly jumps from one value to another. Essential or infinite discontinuities, also known as poles, occur when the function approaches infinity or negative infinity as the input approaches a certain value, resulting in a vertical asymptote on the graph. Understanding epäjatkeisuudet is crucial in calculus and analysis for determining the behavior of functions and for applying theorems that require continuity.