![]() ![]() ![]() We can rewrite the original function like this: Now, we will factor out the denominator using the same above procedure as shown below:Īs we can see that the common factor in the numerator and the denominator is (x + 4). Both the numerator and the denominator can be factored in this example. Hence, the removable discontinuity of the function is at the point x = 4.įind the factors of the numerator and the denominator. We need to set it equal to zero to get the removable discontinuity. Now, we have identified the common factor which is x - 4. Step 3 - Set the common factors equal to zero and find the value of x The denominator cannot be factored further, but we can factor the numerator.Īs we can see that the common factor in the numerator and the denominator is (x - 4). Example 1įind the removable discontinuity of the following function:įollow these steps to identify the removable discontinuity of the above function.įind the factors of the numerator and the denominator. In the next section, we will solve some examples in which we will find the removable discontinuity of a function and plot it on the graph. Step 4 - Plot the graph and mark the point with a hole Step 3 - Set the common factors equal to zero and find the value of x. Step 2 - Determine the common factors in the numerator and the denominator Step 1 - Factor out the numerator and the denominator On the other hand, if adjusting a function's value at a specific point of discontinuity will give a continuous function, then we say that the discontinuity is removable at that point.įollow these steps to solve removable discontinuities. If the limit does not exist at a specific point, then the discontinuity is non-removable at that point. The functions that are not continuous at any value of x either have a removable or a non-removable discontinuity. Difference Between Removable and Non-Removable Discontinuities On the graph, a removable discontinuity is marked by an open circle to specify the point where the graph is undefined. ![]() You can identify this point by seeing a gap where this point is located. Let's go What is Removable Discontinuity?Ī removable discontinuity is defined as follows:Ī point on the graph that is undefined or is unfit for the rest of the graph is known as a removable discontinuity ![]()
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