Mathematics Exam > Mathematics Videos > Calculus > Introduction - Continuity
Introduction - Continuity Video Lecture | Calculus - Mathematics
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FAQs on Introduction - Continuity Video Lecture - Calculus - Mathematics
| 1. What is continuity in mathematics? |  |
Ans. Continuity in mathematics refers to the property of a function or a curve where there are no abrupt changes or breaks. It means that the function or curve can be drawn without lifting the pen from the paper.
| 2. How can continuity be determined for a function? | |
Ans. Continuity of a function can be determined by checking three conditions: the function must be defined at the point in question, the limit of the function at that point must exist, and the limit must be equal to the value of the function at that point.
| 3. What is the importance of continuity in calculus? | |
Ans. Continuity is crucial in calculus because it allows us to analyze and solve problems involving rates of change, optimization, and integration. It ensures that the functions we work with are well-behaved and can be easily manipulated.
| 4. Can a function be continuous at a point but not on an interval? | |
Ans. Yes, a function can be continuous at a single point but not on an interval. This can occur if the function has a removable discontinuity or a jump discontinuity within the interval. Continuity at a point only requires the function to be defined at that point and have a limit that exists.
| 5. What are the different types of discontinuity? | |
Ans. There are three main types of discontinuity: removable discontinuity, jump discontinuity, and essential discontinuity. A removable discontinuity occurs when a function has a hole or gap at a certain point. A jump discontinuity happens when the function has two different finite limits from the left and right sides of a point. An essential discontinuity occurs when the limit of the function does not exist at a point.
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Nov 24, 2024 Last updated |
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