# What is an example of a discontinuous function?

## What is an example of a discontinuous function?

Some of the examples of a discontinuous function are: f(x) = 1/(x – 2) f(x) = tan x. f(x) = x2 – 1, for x < 1 and f(x) = x3 – 5 for 1 < x < 2.

## How do you show a function is discontinuous?

To show from the (ε, δ)-definition of continuity that a function is discontinuous at a point x0, we need to negate the statement: “For every ε > 0 there exists δ > 0 such that |x − x0| < δ implies |f(x) − f(x0)| < ε.” Its negative is the following (check that you understand this!): “There exists an ε > 0 such that for …

What is a discontinuity in a function?

The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

### What are the types of discontinuity of function?

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. They occur when factors can be algebraically removed or canceled from rational functions.

### What are continuous and discontinuous functions with examples?

A function is said to be continuous if it can be drawn without picking up the pencil. Otherwise, a function is said to be discontinuous. Similarly, Calculus in Maths, a function f(x) is continuous at x = c, if there is no break in the graph of the given function at the point.

What is a real life example of a continuous function?

Suppose you want to use a digital recording device to record yourself singing in the shower. The song comes out as a continuous function.

## Can a discontinuous function have a limit?

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. This function is obviously discontinuous at x=0 as it has the limit 0.

## Is a discontinuous function differentiable?

If a function is discontinuous, automatically, it’s not differentiable.

What is simple discontinuity?

1: 1.4 Calculus of One Variable

… ►A simple discontinuity of ⁡ at occurs when ⁡ and ⁡ exist, but ⁡ ( c + ) ≠ f ⁡ . If ⁡ is continuous on an interval save for a finite number of simple discontinuities, then ⁡ is piecewise (or sectionally) continuous on . For an example, see Figure 1.4.

### How do you know 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.

### What is difference between continuity and discontinuity?

Continuity refers to the view that development is a gradual, continuous process. Discontinuity refers to the view that development occurs in a series of distinct stages. A similar debate exists concerning nature versus nurture.

What are 3 examples of discrete data?

Examples of discrete data:

• The number of students in a class.
• The number of workers in a company.
• The number of parts damaged during transportation.
• Shoe sizes.
• Number of languages an individual speaks.
• The number of home runs in a baseball game.
• The number of test questions you answered correctly.

## What type of discontinuity is 0 0?

The graph of the function is shown below for reference. In order to fix the discontinuity, we need to know the y-value of the hole in the graph. To determine this, we find the value of limx→2f(x). The division by zero in the 00 form tells us there is definitely a discontinuity at this point.

## Can discontinuous function be differentiable?

Are all discontinuous function non differentiable?

### Can a function be differentiable everywhere but discontinuous?

The converse of the differentiability theorem is not true. It is possible for a differentiable function to have discontinuous partial derivatives. An example of such a strange function is f(x,y)={(x2+y2)sin(1√x2+y2) if (x,y)≠(0,0)0 if (x,y)=(0,0).

### What are the 3 conditions of continuity?

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.

What are the three types of discontinuity?

Continuity and Discontinuity of Functions
There are three types of discontinuities: Removable, Jump and Infinite.

## What are 5 examples of continuous data?

Examples of continuous data:

• The amount of time required to complete a project.
• The height of children.
• The amount of time it takes to sell shoes.
• The amount of rain, in inches, that falls in a storm.
• The square footage of a two-bedroom house.
• The weight of a truck.
• The speed of cars.
• Time to wake up.

Is age continuous or discrete?

continuous
– Is age discrete or continuous? Age is a discrete variable when counted in years, for example when you ask someone about their age in a questionnaire. Age is a continuous variable when measured with high precision, for example when calculated from the exact date of birth.

### Is 0 continuous or discontinuous?

f(x)=0 is a continuous function because it is an unbroken line, without holes or jumps. All numbers are constants, so yes, 0 would be a constant.

### How do you tell if a function is continuous but not differentiable?

Relationship between Continuity and Differentiability: If a function is differentiable at a point, then it is continuous at that point. However if a function is continuous at a point, it is possible for it to not be differentiable. Differentiability implies continuity, but continuity does not imply differentiability.

Can a point be discontinuous but differentiable?

It is possible for a differentiable function to have discontinuous partial derivatives. An example of such a strange function is f(x,y)={(x2+y2)sin(1√x2+y2) if (x,y)≠(0,0)0 if (x,y)=(0,0).

## Does discontinuity mean not differentiable?

Well, a function is only differentiable if it’s continuous. So if there’s a discontinuity at a point, the function by definition isn’t differentiable at that point.