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Decide whether or not the function is continuous. If it is not continuous, identify the points at which it is discontinuous.$$f(x)=x^{2}+2 x+5$$

Continuous

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Harvey Mudd College

University of Michigan - Ann Arbor

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 this problem. In this problem, we have to decide whether or not the function is continuous. If it is not continuous, we have to identify the points at which it is discontinuous. So the given function is F of X is equal to extra pair plus two x last five. Okay, as the given function is a polynomial function of second degree and we know that all the polynomial functions are continuous everywhere because there is no such a real number for which the function is not defined as we can see from the graph as well. The growth of the function shows a parabola opening upward, and this graph shows that there is no hole for the do men and no brakes are. Jams are no shop cabinet. So by definition of polynomial, we can say that the given function is the human function above X is continuous, continuous everywhere because for a function to be continuous, it's grub should not have any hole, any breaker, jump or any sharp corner. So the group of the given function is a parabola, so we can conclude that the given function is continuous everywhere

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