Difference between revisions of "Math 22 Continuity"
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==Continuity== | ==Continuity== | ||
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| + | Informally, a function is continuous at <math>x=c</math> means that there is no interruption in the graph of <math>f</math> at <math>c</math>. | ||
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| + | ==Definition of Continuity== | ||
| + | Let <math>c</math> be a real number in the interval <math>(a,b)</math>, and let <math>f</math> be a function whose domain contains the interval<math>(a,b)</math> . The function <math>f</math> is continuous at <math>c</math> when | ||
| + | these conditions are true. | ||
| + | 1. <math>f(c)</math> is defined. | ||
| + | 2. <math>\lim_{x\to c} f(x)</math> exists. | ||
| + | 3. <math>\lim_{x\to c} f(x)=f(c)</math> | ||
| + | If is continuous at every point in the interval <math>(a,b)</math>, then <math>f</math> is continuous on the '''open interval''' <math>(a,b)</math>. | ||
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'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 07:43, 16 July 2020
Continuity
Informally, a function is continuous at means that there is no interruption in the graph of at .
Definition of Continuity
Let be a real number in the interval , and let be a function whose domain contains the interval . The function is continuous at when
these conditions are true.
1. is defined. 2. exists. 3. If is continuous at every point in the interval , then is continuous on the open interval .
This page were made by Tri Phan