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L15 : Example derivation- limits and derivatives, Mathematics, Class 11 Video Lecture

FAQs on L15 : Example derivation- limits and derivatives, Mathematics, Class 11 Video Lecture

1. What is the definition of a derivative in calculus?

Ans. The derivative of a function at a specific point is defined as the rate at which the function is changing at that point. It represents the slope of the tangent line to the function's graph at that point.

2. How is the limit used to calculate derivatives?

Ans. The limit is used in calculus to calculate derivatives by taking the limit of the difference quotient as the interval approaches zero. The difference quotient measures the average rate of change of a function over a small interval, and by taking the limit, we can find the instantaneous rate of change or the derivative.

3. What is the relationship between limits and continuity in calculus?

Ans. The concept of limits is closely related to continuity in calculus. A function is 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. In other words, for a function to be continuous, the limit and the value of the function must agree.

4. How can derivatives be used to find maximum and minimum points of a function?

Ans. Derivatives can be used to find maximum and minimum points of a function by analyzing the critical points. A critical point is a point where the derivative of the function is either zero or undefined. By finding the critical points and analyzing the sign of the derivative around those points, we can determine whether they correspond to maximum or minimum points.

5. What is the chain rule in calculus and how is it used to find derivative 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, say f(g(x)), then the derivative of the composite function can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function. The chain rule is a powerful tool for calculating derivatives in more complex scenarios.

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Oct 04, 2025 Last updated

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