NCERT Class 11 Mathematics Mathematics: Chapter 12 — Limits and Derivatives
This chapter introduces Calculus, focusing on the study of how a function's value changes with its domain points. It provides an intuitive understanding of derivatives by examining the velocity of a falling body. Using the formula s = 4.9t², the chapter calculates average velocities over decreasing time intervals approaching a specific point (t=2 seconds). This process illustrates the concept of a limit, showing how the average velocity approaches a specific value as the time interval shrinks. The chapter aims to build a foundational understanding of derivatives and limits, crucial for further mathematical studies in Calculus and its applications in science and engineering, preparing students for advanced topics and problem-solving within the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 12 — Limits and Derivatives |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 574 |
Learning outcomes
- Understand the basic concept of Calculus and its importance.
- Develop an intuitive idea of derivatives through real-world examples like velocity.
- Grasp the concept of limits and how they relate to derivatives.
- Learn to calculate average rates of change.
- Prepare for advanced Calculus topics.
Vocabulary
| Word | Meaning |
|---|---|
| Calculus | A branch of mathematics dealing with rates of change and accumulation. |
| Function | A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. |
| Derivative | The instantaneous rate of change of a function with respect to one of its variables. |
| Limit | The value that a function or sequence 'approaches' as the input or index approaches some value. |
| Average Velocity | The change in position divided by the change in time. |
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Practice questions
- What is the primary focus of Calculus as described in the chapter? Answer: Calculus mainly deals with the study of change in the value of a function as the points in the domain change.
- How is the distance traveled by a body dropped from a cliff modeled in the chapter? Answer: The distance s in metres is modeled as a function of time t in seconds by s = 4.9t².
- What is the formula for average velocity between time t1 and t2? Answer: Average velocity = (Distance traveled between t1 and t2) / (t2 – t1).
Practice MCQs
Q1. Calculus is the branch of mathematics that studies:
Explanation: The chapter defines Calculus as the study of how a function's value changes as its domain points change.
Q2. The formula for the distance traveled by a dropped body is given as:
Explanation: The text explicitly states the distance s in metres covered by the body as a function of time t in seconds is given by s = 4.9t².
Q3. Average velocity is calculated as:
Explanation: The chapter defines average velocity as the distance traveled divided by the time interval (t2 – t1).
Q4. What does the chapter aim to provide an intuitive idea of, without a formal definition initially?
Explanation: The introduction states that the chapter gives an intuitive idea of derivative without actually defining it.
Q5. As the time interval ending at t=2 seconds gets smaller, the average velocity:
Explanation: The text observes that as time intervals get smaller, the average velocity gives a better idea of the velocity at t=2 seconds.
Frequently asked questions
What is Calculus?
Calculus is a branch of mathematics that deals with the study of change in the value of a function as the points in the domain change.
What is the formula for the distance traveled by a body dropped from a cliff?
The distance 's' in meters traveled by a body dropped from a cliff in 't' seconds is given by the formula s = 4.9t².
How is average velocity calculated?
Average velocity is calculated by dividing the distance traveled between two points in time by the difference between those two times (t2 - t1).
What is the main goal of introducing the falling body example?
The example is used to develop an intuitive understanding of how to find the velocity of an object at a specific moment in time, leading to the concept of a derivative.
What does the chapter aim to introduce?
The chapter introduces Calculus, focusing on the concepts of limits and derivatives.
Related resources
Important topics
Topics covered
NCERT Class 11 Mathematics — Mathematics — Chapter 12 — Limits and Derivatives. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.