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Definition & Examples Of Continuity Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
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FAQs on Definition & Examples Of Continuity Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is the definition of continuity in mathematics? |  |
Ans. Continuity in mathematics refers to the property of a function where the graph of the function can be drawn without lifting the pen from the paper. More formally, a function is said to be continuous at a point if the limit of the function at that point exists and is equal to the value of the function at that point.
| 2. How can continuity be visually represented? | |
Ans. Continuity can be visually represented through the graph of a function. A function is continuous if its graph is a single, unbroken curve without any jumps, breaks, or holes. The smoothness and connectedness of the graph indicate the continuity of the function.
| 3. What are the different types of discontinuities that can occur in a function? | |
Ans. There are three main types of discontinuities that can occur in a function: removable, jump, and infinite. Removable discontinuities occur when there is a hole in the graph that can be filled by redefining the function at that specific point. Jump discontinuities occur when there is a sudden jump or gap in the graph, indicating a change in the function's value. Infinite discontinuities occur when the function approaches positive or negative infinity at a certain point.
| 4. How can we determine the continuity of a function at a specific point? | |
Ans. To determine the continuity of a function at a specific point, we need to check three conditions: the function must be defined at that point, the limit of the function as it approaches that point must exist, and the value of the function at that point must be equal to the limit. If all three conditions are satisfied, the function is continuous at that point.
| 5. Can a function be continuous but not differentiable? | |
Ans. Yes, a function can be continuous but not differentiable. Continuity only requires that the function's graph is a single, unbroken curve, while differentiability additionally requires the existence of the derivative at each point. Discontinuities in the derivative may occur even if the function itself is continuous, leading to a situation where a function is continuous but not differentiable.
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Nov 24, 2024 Last updated |
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