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Functions of One Variable: Limits of Functions- 2 Video Lecture | Mathematics for Competitive Exams
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FAQs on Functions of One Variable: Limits of Functions- 2 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 represents the behavior of the function as its input approaches a certain value. It measures the value that the function approaches as the input gets arbitrarily close to a given point.
| 2. How can I determine the limit of a function algebraically? | |
Ans. To determine the limit of a function algebraically, you can use various techniques such as simplifying the expression, factoring, rationalizing, or applying known limit properties like the sum, product, or quotient rules. You can also use algebraic manipulation to rewrite the function in a form that allows you to directly substitute the value into the expression.
| 3. Can a function have a limit at a point where it is not defined? | |
Ans. Yes, a function can have a limit at a point where it is not defined. The limit of a function only depends on the behavior of the function as the input approaches the given point, not the actual value of the function at that point. Therefore, even if the function is not defined at a particular point, it can still have a limit if the nearby values of the function approach a certain value.
| 4. What are some common indeterminate forms when evaluating limits? | |
Ans. Some common indeterminate forms when evaluating limits include 0/0, ∞/∞, 0∙∞, ∞ - ∞, and ∞^0. These forms arise when direct substitution of the limit value into the expression leads to an undefined or ambiguous result. In such cases, additional techniques like L'Hôpital's rule or algebraic manipulation may be required to evaluate the limit accurately.
| 5. Can the limit of a function exist even if the function is not continuous? | |
Ans. Yes, the limit of a function can exist even if the function is not continuous. Continuity refers to the smoothness and lack of any jumps or holes in a function, while the limit focuses on the behavior of the function near a specific point. A function can have a limit at a point where it is not continuous if the left and right limits coincide, even if the function has a jump or a removable discontinuity at that point.
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Dec 23, 2024 Last updated |
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