Quick Answer: Can A Limit Exist If It Is Discontinuous?

Is a function continuous if it has a hole?

The function is not continuous at this point.

This kind of discontinuity is called a removable discontinuity.

Removable discontinuities are those where there is a hole in the graph as there is in this case.

In other words, a function is continuous if its graph has no holes or breaks in it..

How do you know if a point is discontinuous?

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 are continuous and discontinuous functions?

We said above that if any of the three conditions of continuity is violated, function is said to be discontinuous. =>f(x) is discontinuous at –1. However, if we try to find the Limit of f(x), we conclude that f(x) is continuous on all the values other than –1. Limx→-1f(x) = Limx→-1(x2–1)x+1 = Limx→-1(x–1) = (–1–1)=–2.

Is a function continuous at a corner?

doesn’t exist. A continuous function doesn’t need to be differentiable. There are plenty of continuous functions that aren’t differentiable. Any function with a “corner” or a “point” is not differentiable.

What do you do when the limit is 1 0?

The other comments are correct: 10 is undefined. Similarly, the limit of 1x as x approaches 0 is also undefined. However, if you take the limit of 1x as x approaches zero from the left or from the right, you get negative and positive infinity respectively.

What is the limit of a discontinuous function?

Classification of Discontinuity Points All discontinuity points are divided into discontinuities of the first and second kind. There exist left-hand limit limx→a−0f(x) and right-hand limit limx→a+0f(x); These one-sided limits are finite.

How do you know if a limit is continuous or discontinuous?

A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value.

Can 0 be a limit?

In order to say the limit exists, the function has to approach the same value regardless of which direction x comes from (We have referred to this as direction independence). Since that isn’t true for this function as x approaches 0, the limit does not exist.

Does a hole make a graph discontinuous?

We now present examples of discontinuous functions. These graphs have: breaks, gaps or points at which they are undefined. In the graphs below, the function is undefined at x = 2. The graph has a hole at x = 2 and the function is said to be discontinuous.

Does a limit exist at an open circle?

Nope. The open circle does mean the function is undefined at that particular x-value. However, limits do not care what is actually going on at the value. Limits only care about what happens as we approach it.

Where does a limit not exist?

A common situation where the limit of a function does not exist is when the one-sided limits exist and are not equal: the function “jumps” at the point. The limit of f f f at x 0 x_0 x0​ does not exist.

What happens if the numerator is 0?

If the numerator is 0, then the entire fraction becomes zero, no matter what the denominator is! For example, 0⁄100 is 0; 0⁄2 is 0, and so on. The word “numerator” is derived from the Latin word numerātor, which means counter. If the numerator is the same as the denominator, the value of the fraction becomes 1.

Can a limit exist and not be continuous?

3 Answers. No, a function can be discontinuous and have a limit. The limit is precisely the continuation that can make it continuous. Let f(x)=1 for x=0,f(x)=0 for x≠0.