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Limits & Derivatives PPT Maths Class 11
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FAQs on Limits & Derivatives PPT Maths Class 11
| 1. What is the definition of a limit in calculus? |  |
Ans. In calculus, a limit is a value that a function or sequence approaches as the input or index approaches a certain point. It represents the behavior of the function or sequence near that point, whether it approaches a specific value or becomes unbounded.
| 2. How can limits be used to determine the continuity of a function? | |
Ans. Limits play a crucial role in determining the continuity of a function. 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. If the limit and the function value are not equal, the function is discontinuous at that point.
| 3. What is the derivative of a function and how is it calculated? | |
Ans. The derivative of a function represents its rate of change at any given point. It measures how the function's output changes with respect to its input. The derivative of a function f(x) is calculated using the limit process known as differentiation. It involves finding the limit of the difference quotient as the change in x approaches zero.
| 4. How does the chain rule help in finding derivatives of composite functions? | |
Ans. The chain rule is a fundamental rule in calculus that allows us to find the derivative of a composite function. It states that if we have a composition of two functions, f(g(x)), then the derivative of this composite function is the product of the derivative of the outer function, evaluated at the inner function, multiplied by the derivative of the inner function.
| 5. What are the different types of limits that can exist for a function? | |
Ans. There are several types of limits that can exist for a function. Some common types include:
- Finite limits: When the limit of the function exists and is a finite value.
- Infinite limits: When the limit of the function approaches positive or negative infinity.
- One-sided limits: When the limit of the function is approached from only one side, either the left or the right.
- Oscillating limits: When the limit of the function does not exist because it oscillates between different values.
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Nov 21, 2024 Last updated |
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