## Limits and Derivatives |

# Limits and Derivatives NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 13.2 Miscellaneous Free pdf Notes Study Material download-Anand Classes

NCERT solutions for class 11 maths chapter 13 limits and derivatives is an introductory chapter to Calculus. It is that branch of mathematics that mainly deals with the study of the change in the value of a function as the points in the domain change.

# Download the pdf of NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives

# Download the NCERT Book for Class 11 Maths Chapter 13 – Limits and Derivatives

# Number of questions in each exercise of NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives

This chapter starts by giving an intuitive understanding of derivatives and then proceeds to study limits as well as their algebra. This is a very well-written chapter as it will help students build an understanding of various aspects associated with limits and derivatives. It helps them develop deep-seated conceptual knowledge that will stay with them throughout their educational careers. NCERT solutions class 11 maths chapter 13 gives the building blocks for calculus that will be further used in differentiation and integration. Calculus is a subject that is not only required for Mathematics but has a huge impact on other subjects such as Physics, Chemistry, Economics, and Biological Sciences.

Class 11 maths NCERT solutions chapter 13 is laced with many formulas and concepts that keep making their way in other chapters directly or indirectly. Thus, it is important that students go through this chapter with utmost care and due diligence. It seems like a difficult and confusing chapter however, once students start understanding the underlying concepts it is one of the most scoring sections in examinations. Additionally, there are several tricks given in the NCERT solutions Chapter 13 Limits and Derivatives that will help students cross-check their final answer within seconds so as to get an excellent grade. In this article, we will take a look at this chapter in-depth and also download the exercise-wise solutions provided in the links below.

- NCERT Solutions Class 11 Maths Chapter 13 Ex 13.1
- NCERT Solutions Class 11 Maths Chapter 13 Ex 13.2
- NCERT Solutions Class 11 Maths Chapter 13 Miscellaneous Exercise

## NCERT Solutions for Class 11 Maths Chapter 13 PDF

Issac Newton (1642 – 1727) and G.W. Leibnitz (1646 – 1717) are credited with the discovery of Calculus. The rigorous concepts are mainly attributed to mathematicians, A.L. Cauchy, J.L.Lagrange, and Karl Weierstrass. students can learn many other such facts along with well-curated explanations to all the NCERT textbook questions by studying the NCERT solutions class 11 maths. The PDFs to all these solutions can be accessed via the links given below:

### NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

NCERT Solutions Class 11 Maths Chapter 13 limits and derivatives are one of the most important chapters that a child will study throughout his school life as it is the most widely used subject in industrial applications. Thus, students need to make it a point to constantly revise these concepts along with the formulas required in order to master the subject. A detailed analysis of all the exercises in an easy-to-understand language has been given below.

- Class 11 Maths Chapter 13 Ex 13.1 – 32 Questions
- Class 11 Maths Chapter 13 Ex 13.2 – 11 Questions
- Class 11 Maths Chapter 13 Miscellaneous Ex – 30 Questions

# Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives

**Topics Covered:** Right-hand limit, left-hand limit, algebra of limits, limits of trigonometric functions, the derivative formula, algebra of derivative functions, and derivatives of the polynomial as well as trigonometric functions are the topics encompassed in the class 11 maths NCERT solutions chapter 13.

**Total Questions:** Class 11 maths chapter 13 Limits and Derivatives has a total of 73 sums out of which 23 are simple formula-based questions, 20 are medium level and 30 are difficult problems.

Class 11 Maths Chapter 13 Limits and Derivatives in the CBSE Syllabus include the following:

**13.1 Introduction**

This section introduces the branch of Mathematics called calculus, derivative, limits and algebra of limits. Derivatives of certain standard functions are also discussed.

- Calculus is used in electrical engineering to find the length of wire to be used between two stations which are miles apart.
- Calculus is used to find the velocity and trajectory of an object.
- Calculus is used in operations research to improve efficiency and productivity and earn profits.

**13.2 Intuitive Idea of Derivatives**

This section defines the derivative of a function by giving a real-life example of distance travelled at different intervals of time.

The derivative is the rate of change at which one quantity varies concerning another. If one runs a business (say selling candies), derivatives can help one decide what quantity one should sell. The data on the business performance over the past few months is to be taken, and the trend needs to be analysed by plotting a curve. Derivative defines the instantaneous slope (dy/dx) of this graph.

The slope gives an idea of the marginal cost (change in cost/change in unit produced) of producing every additional unit at that instant. If this cost is greater than 10 bucks, that is the selling price, then a loss is incurred at the point.

For better clarity, refer to the table given below.

For 0-300 units, if the cost > sales, then it’s a loss

For 400-600 units, if the sales > cost, then it’s a profit

**13.3 Limits**

This section explains limits with an interesting example, left-hand limit and right-hand limit with solved problems.

If an ice cube is dropped into a glass of warm water and the temperature is measured with time, it is an example of a limit as the time approaches infinity. The time measured here is the temperature slowly attaining the room temperature where the glass was stored.

13.3.1 Algebra of limits

This section demonstrates the output of the sum, difference, product and quotient of limits.

13.3.2 Limits of polynomials and rational functions

The limits of polynomials and rational functions are elaborated on, along with solved examples.

**13.4 Limits of Trigonometric Functions**

This section deals with the theorems and prepositions for functions, which are helpful in calculating the limits of some trigonometric functions.

**13.5 Derivatives**

This section helps the student to find solutions to different derivative problems.

Money-related establishments need to anticipate the adjustments in the estimation of a specific stock knowing its present worth. In this, and numerous such cases, it is important to know how a specific parameter is changing in accordance with the other parameter. The heart of the text is the derivative of a function at a given point in its domain of definition.

13.5.1 Algebra of derivatives of functions

This section demonstrates the output of the sum, difference, product and quotient of derivatives.

13.5.2 Derivative of polynomials and trigonometric functions

This section deals with the theorems and problems for functions which help calculate the derivatives of some trigonometric functions.

# List of Formulas in NCERT Solutions Class 11 Maths Chapter 13 – Limits and Derivatives

NCERT solutions class 11 maths chapter 13 is mainly based on formulas and the conceptual understanding of them. These are crucial as it helps to simplify sums that would otherwise prove to be very difficult to solve. students should first try to understand the ideology and the derivations of these formulas before memorizing them. As there will be umpteen formulas that will fall under the topic of calculus hence, it is highly recommended that students make a formula chart that will help them get a quick overview of the chapter. Some of the important formulas that are covered in this chapter are given below.

- lim
_{x → a}(x^{n}– a^{n}) / x – a = na^{n-1} - lim
_{x → a}sinx / x = 1 - lim
_{x → a}1 – cosx / x = 0 - f ´( x ) = d f(x)/dx = lim
_{h → 0}[ f(x+h) – f(x) / h]

# Frequently Asked Questions (FAQs) on NCERT Solutions Class 11 Maths Chapter 13 – Limits and Derivatives

**Q1**

### Why are NCERT Solutions Class 11 Maths Chapter 13 Important?

The NCERT Solutions Class 11 Maths Chapter 13 are written in a step-wise manner with a detailed explanation for each computation performed. students are not only able to develop a strong understanding of the topic but they also get an idea of how to present their papers in an examination to get the best possible score.

**Q2**

### Do I Need to Practice all Questions Provided in Class 11 Maths NCERT Solutions Limits and Derivatives?

All the sums in the 3 exercises in the NCERT Solutions Class 11 Maths Limits and Derivatives cover different aspects of the chapter. The questions are available in a variety of formats that help students explore the types of sums that can appear on an exam. Thus, it is essential for students to practice all problems so as to get a clear understanding of the subject matter.

**Q3**

### What are the Important Topics Covered in NCERT Solutions Class 11 Maths Chapter 13?

The most important topics in the NCERT Solutions Class 11 Maths Chapter 13 are calculating the limits of a function as well as the algebra of limits and derivatives. The procedures for computing these values will be used in upcoming chapters and thus, students need to allot a good amount of time to prepare this subject matter.

**Q4**

### How Many Questions are there in NCERT Solutions Class 11 Maths Chapter 13 Limits and Derivatives?

There are 73 exemplar problems in the NCERT Solutions Class 11 Maths Chapter 13 Limits and Derivatives. These are divided into 3 exercises out of which one is miscellaneous consisting of higher-order questions. They help students get an overall understanding of the chapter in-depth and range from simple to complex sums.

**Q5**

### How CBSE Students can utilize Class 11 Maths NCERT Solutions Chapter 13 effectively?

To utilize the NCERT Solutions Class 11 Maths Chapter 13 students need to meticulously go through the theory enlisted in each section. The next step is to study all the formulas and understand the derivations. Finally, students can apply these to the range of questions available in the NCERT textbooks.

**Q6**

### Why Should I Practice NCERT Solutions Class 11 Maths Limits and Derivatives Chapter 13?

Practice makes a person perfect his art. As this is one of the most crucial chapters students need to understand each concept and learn to apply them in an effective way. Additionally, students also understand how to attempt their examination papers in an efficient way. Thus, they need to revise these solutions and time themselves while attempting these problems so as to ace their exams.

**Q7**

### What are the topics included in Chapter 13 of NCERT Solutions for Class 11 Maths?

Students must first understand the topics included in Chapter 13 of NCERT Solutions for Class 11 Maths to lay a strong foundation of differentiation and integration. The topics covered in this chapter are as follows:

1. Introduction

2. Intuitive Idea of Derivatives

3. Limits

4. Limits of Trigonometric Functions

5. Derivatives

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