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Functions of One Variable: Limits of Functions- 1 Video Lecture | Mathematics for Competitive Exams
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FAQs on Functions of One Variable: Limits of Functions- 1 Video Lecture - Mathematics for Competitive Exams
| 1. What is the definition of a limit of a function? |  |
Ans. The limit of a function is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It determines the value that the function tends to approach as the input gets arbitrarily close to a particular point.
| 2. How do you evaluate the limit of a function algebraically? | |
Ans. To evaluate the limit of a function algebraically, you can use various techniques such as direct substitution, factoring, rationalizing, or applying algebraic manipulation. These methods help simplify the function or transform it into a form that allows you to substitute the desired value into the function and find the limit.
| 3. Can the limit of a function exist even if the function is not defined at that point? | |
Ans. Yes, it is possible for the limit of a function to exist even if the function is not defined at that point. The limit considers the behavior of the function around the point of interest, rather than the actual value of the function at that point. As long as the function approaches a specific value as the input approaches the given point, the limit exists.
| 4. What are the different types of limits? | |
Ans. There are several types of limits, including:
- Finite limits: These limits have a specific finite value as the input approaches a certain point.
- Infinite limits: These limits indicate that the function tends to approach positive or negative infinity as the input approaches a particular point.
- One-sided limits: These limits focus on the behavior of the function from one direction only, either approaching from the left or the right of a given point.
- Oscillating limits: These limits show that the function oscillates between two or more values as the input approaches a particular point.
| 5. How can you use limits to determine the continuity of a function? | |
Ans. Limits play a crucial role in determining the continuity of a function. A function is continuous at a point if the limit of the function exists at that point and is equal to the value of the function at that point. In other words, the function has no abrupt jumps, holes, or vertical asymptotes at that specific point. By evaluating the limits from both sides of a point and comparing them to the function's value at that point, you can determine if the function is continuous.
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Dec 23, 2024 Last updated |
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