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liq [111]
1 year ago
6

Explain the meaning of continuity as it pertains to a function. Identify and explain the three conditions that must exist in ord

er for a function to be continuous at a given point.
Mathematics
1 answer:
vesna_86 [32]1 year ago
6 0

When there are no gaps or breaks on the graph, a function is continuous. When a function fails to be continuous, it is said to be discontinuous at that location.

<h3>What is Continuity in Calculus?</h3>

A function is continuous when there are no gaps or breaks in the graph. These gaps or breaks can be easily seen in a graph. They are also easily stated as holes, jumps, or vertical asymptotes. However, in calculus, you must be more specific in your definition of continuity.

There are three conditions that must be met in order to state a function is continuous at a certain point.

A function f(x) is continuous at a point a if only if the following three conditions are satisfied:

1.)f(a) is defined

2.)lim x→a f(x) exists

3.)lim x→a f(x)=f(a)

Therefore,  A function is discontinuous at a point a if it fails to be continuous at a.

Learn more about Continuity here

brainly.com/question/24898810

#SPJ1

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- The area of the circle is:

 A=πr²

 A is the area of the circle.
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 r is the radius of the circle.

 - To calculate the area of <span> the sector indicated in the problem, you must apply the following formula:

 As=(</span>θ/2π)πr²

 As is the area of the sector.
 θ is the central angle (θ=2π/9)
 π=3.14
 r is the radius.

 - First, you must find the radius:

 r=Diameter/2
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 - Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:

 As=(θ/2π)πr²
 As=(2π/9/2π)(π)(10.3)²
 As=(π/9π)(π)(10.3)²
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 - Finally, the area of the sector is:

 As= 37.01 mm²
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