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Sketch the graph of a function $ f $ that is continuous except for the stated discontinuity.

Discontinuous, but continuous from the right, at 2.

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The graph of $y=f(x)$ must have a discontinuity at$x=2$ and must show that $\lim _{x \rightarrow 2^{+}} f(x)=f(2)$

01:19

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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Okay in this problem we want to graph a function F of X that is uh discontinuous at two. So the function is going to be discontinuous at two, but it is going to be continuous from the right at two. So in other words, as X is approaching two from the right side, the function is continuous lift draw um a possible function in blue. So Coming in from the right, X is approaching two, It's continuous from the right side at two. So that means uh that the function is to find at two. Um and continuous set to so as to function um the limit of the function as X approaches to equals the value of the function at two. So here's the function continuous from the right at two, But overall the function is discontinuous at two. so for X values to the left of two, we wanted this continuity at two. So let's put an open circle here above X equals two and let's continue DeGraff for X values. Uh less than two. So here is a function F of X. Discontinuous set to, But it was continued continuous from the right at two.

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