Question

How can you tell if a discontinuity of a limit is removable or not removable?

Answer 1

To decide whether an intermittence of a cutoff is removable or not, examine the way of behaving of the capability close forthright. On the off chance that the capability moves toward a limited worth, the brokenness is removable. If it approaches vastness or has no limited worth, the irregularity isn't removable.

Step-by-step explanation:

To decide if an intermittence of a cutoff is removable or not, we want to investigate the way of behaving of the capability close to the mark of brokenness. If the capability moves toward a limited worth as it comes to the heart of the matter, then, at that point, the brokenness is removable. This implies that we can rethink or fill in the worth by then to make the capability persistent.

Then again, if the capability approaches endlessness, or negative vastness, or approaches no limited worth as it comes to the heart of the matter of brokenness, the irregularity isn't removable. This implies that the capability can't be reclassified to make it constant by then.

For instance, consider the capability f(x) = (x² - 1)/(x - 1). At x = 1, the capability is vague. Be that as it may, assuming we improve on the capability by counterbalancing the normal element of (x - 1), we get f(x) = x + 1. As x methodologies 1, the capability approaches 2. Accordingly, the brokenness at x = 1 is removable.

Answer 2

A discontinuity is present if any of ...

• the limit doesn't exist
• the limit is not the same as the value of the function

If the one of these that is the cause of discontinuity is the last one and defining the function will make this issue go away, then the discontinuity is removable.