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What conditions must be satisfied for a function to be continuous

User OllyBarca
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1 Answer

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15 votes

0. This function needs to be defined at one given point.

,

1. There must be a limit for this function

,

2. The value of the, limit of that function, at that point must be the same as the, value of that function, at that point.

1) There are three conditions that must be satisfied so that we can tell that one given function is continuous at a given point.

2) This function needs to be defined at one point, in other words, there must be a value linking that point in the Domain to another one in the Range.

There must be a limit as x approaches that point from left and from the right.

Finally, the value of the limit of that function as x approaches that point must be the same as the value of that point.

3) Hence, the answer is:

0. This function needs to be defined at one given point.

,

1. There must be a limit for this function

,

2. The value of the limit must be the same as the value of that function at that point.

User Iamnat
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2.3k points