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Functions of One Variable: Continuous Functions Video Lecture | Mathematics for Competitive Exams
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FAQs on Functions of One Variable: Continuous Functions Video Lecture - Mathematics for Competitive Exams
| 1. What is a continuous function? |  |
Ans. A continuous function is a mathematical function that does not have any abrupt changes or jumps in its graph. In other words, it is a function that can be drawn without lifting the pen from the paper.
| 2. How can we determine if a function is continuous? | |
Ans. To determine if a function is continuous, we need to check three conditions: 1) The function is defined at the point of interest, 2) The limit of the function exists at that point, and 3) The limit of the function is equal to the value of the function at that point. If all three conditions are satisfied, then the function is continuous at that point.
| 3. Can a continuous function have a vertical asymptote? | |
Ans. No, a continuous function cannot have a vertical asymptote. A vertical asymptote occurs when the function approaches infinity or negative infinity as it approaches a certain value of x. Since a continuous function does not have abrupt changes or jumps, it cannot approach infinity or negative infinity in such a way that a vertical asymptote is formed.
| 4. Are all polynomials continuous functions? | |
Ans. Yes, all polynomials are continuous functions. A polynomial is an algebraic expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents. Since polynomials are defined for all real numbers, they satisfy the conditions for continuity and hence are continuous functions.
| 5. Can a continuous function have a removable discontinuity? | |
Ans. No, a continuous function cannot have a removable discontinuity. A removable discontinuity occurs when there is a hole in the graph of the function at a certain point. However, for a function to be continuous, it should not have any abrupt changes or jumps, including holes. Therefore, a continuous function cannot have a removable discontinuity.
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Dec 23, 2024 Last updated |
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