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Interval & Types of Intervals Video Lecture | Mathematics for Competitive Exams
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FAQs on Interval & Types of Intervals Video Lecture - Mathematics for Competitive Exams
| 1. What is an interval in mathematics? |  |
Ans. In mathematics, an interval is a set of real numbers that includes all the numbers between any two given numbers. It can be represented in different forms such as closed interval [a, b], open interval (a, b), half-open interval [a, b), or half-open interval (a, b].
| 2. What is the difference between a closed interval and an open interval? | |
Ans. A closed interval includes both of its endpoints, while an open interval does not include its endpoints. For example, the closed interval [0, 5] includes the numbers 0 and 5, while the open interval (0, 5) includes all the numbers between 0 and 5, excluding 0 and 5.
| 3. What are the types of intervals in mathematics? | |
Ans. There are four types of intervals in mathematics: closed interval, open interval, half-open interval, and half-closed interval. A closed interval includes both of its endpoints, an open interval does not include its endpoints, a half-open interval includes one endpoint and excludes the other, and a half-closed interval includes one endpoint and includes the other.
| 4. How are intervals represented in set notation? | |
Ans. Intervals can be represented in set notation as follows:
- Closed interval: [a, b] = {x | a ≤ x ≤ b}
- Open interval: (a, b) = {x | a < x < b}
- Half-open interval: [a, b) = {x | a ≤ x < b} or (a, b] = {x | a < x ≤ b}
| 5. What are some real-life applications of intervals? | |
Ans. Intervals have various real-life applications, such as:
- Time intervals: Representing durations between events or time periods.
- Temperature intervals: Showing the range of temperatures between two points.
- Confidence intervals: Estimating the range of values for a population parameter based on sample data.
- Stock market intervals: Analyzing the price range of stocks during a specific time period.
- Music intervals: Describing the pitch difference between two musical notes.
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Dec 23, 2024 Last updated |
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