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Decide whether the function whose graph is shown is continuous. If it is not continuous, identify the $x$ -values at which it is discontinuous and classify the discontinuity.Figure 10

$x=2$ and 3

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Missouri State University

Campbell University

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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in problem in exercise therapy. Eight. The growth of the function is given as the Figure 10 shows the growth of the function. For this problem, we had to decide whether the function is continuous or not. So why definition when the graph is given? Ah, function is said to be continuous, as if a golf is continuous or a good office continuous. If it has no holes, breaks or them tops. So is the graph is the figure shows that is. The figure shows that at and at X is equal to and and add X is equal to three. There are breaks if okay, ah graph has breaks. It means that it means that right, left hand side limit, it's not equal to mhm. Right hand side limit. Yeah, for continued the off a function the Arctic. There are three conditions that the second condition for continue it is left hand side limit should be equal to right hand side limit. Then we can say that limit off the function at a particular point exist. So if a graph has breaks, it means that limit does not exist. And if limit does not exist, it means that the function is not continuous, and such continue to such discontinuities cannot be removed. This is called non memorable discontinuity. When graph are figure, has Drax.

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