# Which of the dicontinuities are removable?

• screamtrumpet
In summary, a removable discontinuity, also known as a removable singularity, is a type of discontinuity in a function where the limit exists but the value of the function does not exist at that point. It can be identified by looking at the graph of the function or by finding the limit of the function as it approaches the point of discontinuity. Various factors can cause a removable discontinuity, but it can be removed by filling in the hole or gap at the point of discontinuity. Removable discontinuities do not affect the overall behavior of a function, but if not removed, they can affect the behavior at that specific point.
screamtrumpet

## Homework Statement

Find the x values if any for which x is not continuous.Which of the dicontinuities are removable?

f(x)=1/(x^2+1)

## The Attempt at a Solution

Its unfactorable at the bottom ,i tried to factor it.Would this mean there are no discontinuities?

Are you sure you wrote down the problem correctly. It is undefined when the denominator is zero but x^2 + 1 is never zero. Or maybe the answer is that it is continuous everywhere.

thanks

## 1. What is a removable discontinuity?

A removable discontinuity, also known as a removable singularity, is a type of discontinuity in a function where the limit exists but the value of the function does not exist at that point. This means that the function has a hole or gap at that point, but it can be filled in to make the function continuous.

## 2. How can I identify a removable discontinuity?

A removable discontinuity can be identified by looking at the graph of the function. It appears as a hole or gap in the graph, where the function is undefined at that point. It can also be identified by finding the limit of the function as it approaches the point of discontinuity, if the limit exists but the function value does not, then it is a removable discontinuity.

## 3. What causes a removable discontinuity?

A removable discontinuity can be caused by various factors, such as a simplification error in algebraic expressions, or a removable singularity in a rational function. It can also be caused by piecewise functions, where different pieces of the function have different domains and do not match up at the point of discontinuity.

## 4. Can a removable discontinuity be removed?

Yes, a removable discontinuity can be removed by filling in the hole or gap at the point of discontinuity. This can be done by simplifying the algebraic expression or by adjusting the function to make it continuous at that point. Once the discontinuity is removed, the function becomes continuous and behaves smoothly at that point.

## 5. How do removable discontinuities affect the behavior of a function?

Removable discontinuities do not affect the overall behavior of a function. They only create a small gap or hole in the graph at the point of discontinuity. However, if the discontinuity is not removed, it can affect the behavior of the function at that particular point, as the function is not defined at that point.

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