NCERT Solutions for Limits and Derivatives Exercise 13.1 Class 11 Maths

Exercise 13.1 Class 11 Maths NCERT Solutions: In this article, we have provided NCERT Solutions for Class 11 Maths Chapter 13 Exercise 13.1. Chapter 13 of Class 11 Maths is about Limits and Derivatives. The NCERT solutions provided here on this page are created by experts at Embibe in complete accordance with CBSE guidelines. Hence, students can refer to these solutions in the final exam without any issues.

Students of CBSE Class 11 who are looking for accurate and easy-to-understand answers to Maths Chapter 13 exercises should refer to this article. Since the NCERT syllabus is followed by many state boards as well, students from various state boards can take the help of solutions provided here. In this article, we have provided the NCERT Solutions for Class 11th Limits and Derivatives solutions in PDF format so that students can download and study offline. Scroll down to learn more!

NCERT Solutions for Limits and Derivatives Ex 13.1 Class 11 Maths

We have provided NCERT Solutions for Class 11 Maths Chapter 13 Ex 13.1 in PDF format for offline study of students. These answers and solutions will not only help them in clearing their doubts but also help them score maximum marks in the final exam. Students are advised to go through these solutions if they are stuck somewhere while solving the exercise questions by themselves. Below we have provided a brief overview of the NCERT Solutions for Limits and Derivatives chapter for your reference:

NCERT Solutions for Class 11 Maths Chapter 13 Ex 13.1 PDF Download

Students can download the Limits and Derivatives Class 11 solutions in PDF format to study offline. Many students do not have access to a proper internet connection all the time. Hence, it is always recommended to download the full solutions in PDF. Moreover, you can also take a printout if you want these solutions in paper format. Students are advised to bookmark this page as well for future reference. 

Questions from this chapter are asked in various entrance exams like JEE Main, BITSAT and other state CETs. Hence, download these solutions in PDF and solve the exercise questions. In the table below, you can find the direct PDF links for Ex 13.1 Class 11 Maths.

About NCERT Solutions for Class 11 Maths Ex 13.1

NCERT Class 11 Maths Chapter 13 Exercise 13.1 deals with the introduction of limits, derivatives and limits of trigonometric functions. In this exercise, students learn that it is possible to calculate the rate at which a body’s location changes by knowing its position at various time intervals.

The questions in Ex 13.1 cover topics from Exercise 13.1 to 13.4. Let us see some important points discussed in Exercise 13.1:

13.1: Introduction

This section introduces the calculus, derivative, limits, and algebra of limits branches of mathematics. Certain standard functions’ derivatives are also discussed. Important points are listed below:

1. In electrical engineering, calculus is used to determine the length of wire to be used between two stations that are kilometres apart.
2. Calculus is used to determine an object’s velocity and trajectory.
3. In operations research, calculus is utilised to increase efficiency, productivity, and profit.

13.2: Intuitive Idea of Derivatives

This section explains how to calculate the derivative of a function using a real-life example of distance travelled at various time intervals. The derivative is the rate of variation of one quantity in relation to another. If you run a business (for example, selling sweets), derivatives can assist you to figure out how much to sell.

Data on your company’s success over the last few months should be collected, and the trend should be plotted using a curve. The instantaneous slope (dy/dx) of this graph is defined by derivative.

13.3: Limits

This section covers left-hand and right-hand limits, as well as solved problems on limits. When an ice cube is thrown into a glass of hot water and the temperature is recorded over time, it is an illustration of a limit as time approaches infinity. The temperature steadily reaches the room temperature where the glass was stored during the time period monitored.

13.4: Limits of Trigonometric Functions

This section covers function theorems and prepositions, which are useful in determining the limits of several trigonometric functions.

About NCERT Solutions for Class 11 Maths Chapter 13 Exercise 13.1

Here in this chapter, we will study how the values of a function change as it changes its position at different instants of time.

What are the limits?

In mathematics, a limit is a value that approaches some value.

Consider the function f(x) = x2

Here, x takes values very close to 0, so the value of f(x) also moves towards zero.

We can say that, x0f(x)=0

In general:

As xa, f(x)l, then then l is called the limit of the function f(x) which is symbolically written as xaf(x)=l

For all the limits, the value at which function should assume at a given point x=a did not really depend on how is x tending to a. There are two ways x could approach a number a, either from the left or from the right, i.e., all the values of x near a could be less than a or could be greater than a.

The two types of limits – the right-hand limit and the left-hand limit describe how x approaches a.

1. The value of the right-hand limit of a function f(x) is decided by the values of f(x) when x tends to a from right.
2. The value of the left-hand limit of a function f(x) is decided by the values of f(x) when x tends to a from left.

If the right and the left-hand limits coincide, we call that common value the limit of f(x) at x = a and denote it by xaf(x)

What are Derivatives?

A derivative is a way to show the rate of change, i.e., the rate by which a function is changing at a given point. For example, 

• People maintaining a reservoir need to know when the reservoir will overflow knowing the depth of the water at several instances of time.
• Rocket scientists need to compute the precise velocity with which the satellite needs to be shot out from the rocket knowing the height of the rocket at various times. 
• Financial institutions need to predict the changes in the value of a particular stock knowing its present value.

Benefits of Studying from NCERT Solutions for Class 11 Maths Chapter 13

Studying from Embibe’s Class 12 Maths NCERT Solutions has a number of advantages. Some of the advantages of using Embibe’s NCERT Solutions are listed below:

1. Embibe’s NCERT Solutions are updated to reflect the current CBSE criteria.
2. Embibe’s Maths Class 12 NCERT Solutions are written by top subject specialists (SMEs). The SMEs break down all of the NCERT Class 12 Maths concepts into simple terms.
3. The NCERT Solutions are detailed, allowing students to obtain a thorough knowledge of the material.
4. Embibe’s NCERT Solutions are available for. Students can get the NCERT Solutions for Class 12 Maths for.
5. Embibe’s NCERT Solutions include all of the in-text questions found in CBSE textbooks.
6. Embibe’s Maths NCERT Solutions for Class 12 also assist students in effectively preparing for competitive exams.
7. Embibe’s NCERT Solutions for Maths take a step-by-step approach that makes it easy for pupils to grasp the concepts. This also aids pupils in understanding how to tackle a specific subject or difficulty.
8. NCERT Solutions also assists kids in completing homework assignments on time. It also aids pupils in effectively preparing for exams.
9. Embibe’s NCERT Solutions are comprehensive in nature, ensuring that no topic or concept covered in the NCERT textbooks is overlooked.
10. Embibe’s NCERT Solutions provide a variety of questions that help students study thoroughly for their exams. It includes short answers, long answer questions, MCQs, and other questions that help students prepare for exams.

FAQs on NCERT Solutions for Chapter 12 Class 11 Maths

We have provided some of the frequently asked questions on NCERT Solutions for Chapter 13 Class 11 Maths:

Q.1. Where to get NCERT Solutions for Chapter 13 Exercise 13.1 Class 11 Maths?
Ans: Embibe provides students with, thorough, accurate, and easy-to-understand NCERT Solutions for Class 11 Maths Chapter 13 Ex 13.1. All NCERT Solutions are available in PDF format on Embibe, so students can refer to them and study them offline.

Q.2. Are NCERT Solutions for Class 11 Maths Exercise 13.1 Solutions enough for CBSE Class 11 final exams?
Ans: Yes. NCERT Solutions for Class 11 Maths Chapter 13 Exercise 13.1 is sufficient for CBSE Class 11 final exams.

Q.3. What are some of the preparation tips to score good marks in CBSE Class 12 Board exams?
Ans: By learning and practising all of the in-exercise questions, students can get good marks in CBSE Class 11 exams. Students should make sure that they have the syllabus in hand and that they understand all of the CBSE Class 11 topics thoroughly. They can also use last year’s question papers to better manage their time.

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