What is the difference between removable and nonremovable discontinuity

This does not "remove" the discontinuity. If you factorise the bottom one, no factors will cancel. Click to expand JeffM Elite Member. Joined Sep 14, Messages 6, The first example IS an example of a rational function with a removable discontinuity. HallsofIvy Elite Member. Joined Jan 27, Messages 7, You don't seem to understand what JeffM said. There is no new value for f 0 that will make that continuous.

HallsofIvy said:. So, removable discontinuity fills in the hole in the graph of the function by redefining the original function given. JeffM said:. Jim H. Nov 9, See the explanation below. Explanation: Geometrically, a removable discontinuity is a hole in the graph of f.

Related questions How do you find discontinuity algebraically? How do you find discontinuity of a piecewise function? How do you find discontinuity points? What is the difference between a removable and non removable discontinuity? If the limit does not exist, then the discontinuity is non—removable. Continuity and Discontinuity of Functions Functions that can be drawn without lifting up your pencil are called continuous functions.

You will define continuous in a more mathematically rigorous way after you study limits. There are three types of discontinuities: Removable, Jump and Infinite. The term removable discontinuity is sometimes an abuse of terminology for cases in which the limits in both directions exist and are equal, while the function is undefined at the point x0.

A function has a removable discontinuity if it can be redefined at its discontinuous point to make it continuous. See Example. Removable discontinuities are characterized by the fact that the limit exists. The other types of discontinuities are characterized by the fact that the limit does not exist.

If a discontinuity is not removable, it is essential. In Plain English: A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values. In Plain English: A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers. Money does not have this property — there is always an indivisible unit of smallest currency.