How do you find the points of discontinuity in calculus?

Start by factoring the numerator and denominator of the function. A point of discontinuity occurs when a number is both a zero of the numerator and denominator. Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.

What is a point of discontinuity in calculus?

Any point at which a function fails to be continuous is called a discontinuity.

What is an example of a discontinuity?

Discontinuous Function Examples Example 1: Identify if the function f(x) = (x – 2)/(x – 4) is a discontinuous function. Solution: As we can see, the function f(x) = (x – 2)/(x – 4) is not defined at x = 4. Hence it is discontinuous at x = 4.

Are points of discontinuity and holes the same?

Not quite; if we look really close at x = -1, we see a hole in the graph, called a point of discontinuity. The line just skips over -1, so the line isn’t continuous at that point. It’s not as dramatic a discontinuity as a vertical asymptote, though. In general, we find holes by falling into them.

Is a point of discontinuity the same as a hole?

Not quite; if we look really close at x = -1, we see a hole in the graph, called a point of discontinuity. The line just skips over -1, so the line isn’t continuous at that point. It’s not as dramatic a discontinuity as a vertical asymptote, though.

What are the points of discontinuity?

A point of discontinuity is a RESTRICTION; where the denominator equals zero because it breaks the graph at that point.

How do you find the type of discontinuity?

Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value. Jump discontinuity is when the two-sided limit doesn’t exist because the one-sided limits aren’t equal. Asymptotic/infinite discontinuity is when the two-sided limit doesn’t exist because it’s unbounded.