Which discontinuity is removable

Stover, Christopher. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.

MathWorld Book. Wolfram Web Resources ». Removable Discontinuity: A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. When graphed, a removable discontinuity is marked by an open circle on the graph at the point where the graph is undefined or is a different value like this.

There are two ways a removable discontinuity can be created. Do you see it? A hole in a graph. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point. Formally, a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point; this may be because the function does not exist at that point.

If the function factors and the bottom term cancels, the discontinuity at the x -value for which the denominator was zero is removable, so the graph has a hole in it. After canceling, it leaves you with x — 7. Figure b shows the graph of g x. Next, using the techniques covered in previous lessons see Indeterminate LimitsFactorable we can easily determine. Now we can redefine the original function in a piecewise form:. The first piece preserves the overall behavior of the function, while the second piece plugs the hole.

When a function is defined on an interval with a closed endpoint, the limit cannot exist at that endpoint. From the left, the function has an infinite discontinuity, but from the right, the discontinuity is removable.

Since there is more than one reason why the discontinuity exists, we say this is a mixed discontinuity. Free Algebra Solver What are the types of Discontinuities?