Difference between revisions of "Math 22 Continuity"
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==Definition of Continuity== | ==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. | + | these conditions are true. |
1. <math>f(c)</math> is defined. | 1. <math>f(c)</math> is defined. | ||
2. <math>\lim_{x\to c} f(x)</math> exists. | 2. <math>\lim_{x\to c} f(x)</math> exists. | ||
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 .
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