How do you find the number of points of discontinuity?

Explanation: 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.

What is the set of points of discontinuity of F defined by log x 1?

Answer. C. Clearly, f(x) is not defined at x=0, 1,-1. At all points f(x) is continuosu. Hence, required set is {-1,0,1}

Does 1 x have a point of discontinuity?

The function 1/x is continuous on (0, ∞) and on (−∞, 0), i.e., for x > 0 and for x < 0, in other words, at every point in its domain. However, it is not a continuous function since its domain is not an interval. It has a single point of discontinuity, namely x = 0, and it has an infinite discontinuity there.

Is there a limit when there is discontinuity?

A removable discontinuity exists when the limit of the function exists, but one or both of the other two conditions is not met. In other words, limx→c+f(x)=∞, or one of the other three varieties of infinite limits. If the two one-sided limits have the same value, then the two-sided limit will also exist.

What are points of discontinuity on a graph?

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

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.

What is the domain of log X?

Therefore, the domain of logx is all positive real numbers, or written symbolically it is x∈(0,∞) .

How many types of discontinuity are there?

Summary. There are two types of discontinuities: removable and non-removable. Then there are two types of non-removable discontinuities: jump or infinite discontinuities. Removable discontinuities are also known as holes.

How do you find the points of discontinuity on a graph?

Quick Overview

1. On graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines help us identify discontinuities.
2. As before, graphs and tables allow us to estimate at best.
3. When working with formulas, getting zero in the denominator indicates a point of discontinuity.