Quick Answer: Do Discontinuous Functions Have Limits?

Does a hole make a function discontinuous?

Discontinuous functions are functions that are not a continuous curve – there is a hole or jump in the graph..

When can a limit not exist?

When approaching the limits from the different direction, if one value is not close to another value, we say that the limits do not exist.

Can a function be continuous and not differentiable?

In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

Which function is not continuous Brainly?

The function which is not continuous is C. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls. The reason for this is because the number of these balls is discreet, not continuous (meaning that there cannot be 6.5 balls).

Can there be a limit at a discontinuity?

A finite discontinuity exists when the two-sided limit does not exist, but the two one-sided limits are both finite, yet not equal to each other. The graph of a function having this feature will show a vertical gap between the two branches of the function.

Can a non continuous function have a limit?

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.

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 a graph be continuous with 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.