NCERT Solutions for Class 11 Maths Chapter 12 Limits and Derivatives in Hindi and English Medium updated for new CBSE session 2024-25. Class 11 Maths chapter 12 solution is revised and modified as per the rationalised textbooks issued by NCERT for academic year 2024-25.

**NCERT Solutions for Class 11 Maths Chapter 12 in English Medium**

Class 11 Maths Exercise 12.1 in English

Class 11 Maths Exercise 12.2 in English

Class 11 Maths Misc. Exercise 12 in English

**NCERT Solutions for Class 11 Maths Chapter 12 in Hindi Medium**

Class 11 Maths Exercise 12.1 in Hindi

Class 11 Maths Exercise 12.2 in Hindi

Class 11 Maths Misc. Exercise 12 in Hindi

**Related Links**

Class 11 Maths NCERT Solutions

Class 11 all Subjects NCERT Solutions

## NCERT Solutions for Class 11 Maths Chapter 12

All intermediate (class xi) students of CBSE Board, UP Board, MP Board, Gujrat Board, Uttarakhand Board and Bihar board, who are using books from NCERT (https://ncert.nic.in/) website as their course books, can use these solutions. Download UP Board Solutions and NCERT Solutions Offline Apps of other subjects are also given to download free without any login and password.

Class: 11 | Mathematics |

Chapter 12: | Limits and Derivatives |

Number of Exercises: | Three (2 + Miscellaneous) |

Content: | Exercises and Supplementary Solution |

Mode: | Text and Online Videos |

Academic Year: | CBSE 2024-25 |

Medium: | Hindi and English Medium |

### 11th Maths Chapter 12 Solutions

NCERT Solutions for Class 11 Maths Chapter 12 Limits and Derivatives given below to use free online or download in PDF format for new academic session. Join the Discussion Forum to discuss your doubts related to education and study.

#### Important Terms Related to Limits & Derivatives

Limits: Meaning of x approaches (x->a): Let x be a variable and ‘a’ be a fixed number. If x assumes a succession of values nearer and nearer to ‘a’, it is said to approach ‘a’. We mean that x assumes successively values [neither greater nor less than a] there is no end to this process of coming nearer and nearer to ‘a’.

In this process (x – a) becomes smaller and smaller and can be made as small as we like. We express this by saying that |x – a| become smaller than δ, where δ is an arbitrary number which may be as very small as we please.

##### Concept of Limit

1. Definition of x ->a: Let x be a variable and ‘a’ be a fixed number. Given a positive number δ however small it may be, if x assumes values such that 0 < |x – a| < δ, then we say x tends to ‘a’ and write x ->a.

### Important Questions on 11th Maths Chapter 12

### Evaluate the Given limit: lim(x→3): x+3

lim x→3: x+3

= 3 + 3

= 6

### Find the derivative of x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n for some fixed real number a.

Let f = x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n

∴ f’ = d/dx(x^n+ax^(n-1)+a^2 x^(n-2)+⋯+a^(n-1) x+a^n)

= d/dx (x^n )+a d/dx (x^(n-1) )+a^2 d/dx (x^(n-2) )+⋯+(a^(n-1 ) d)/dx (x)+a^n d/dx (1)

On using theorem d/dx x^n=nx^(n-1) ,we obtain

f’(x) = nx^(n-1)+a(n-1) x^(n-2)+a^2 (n-2) x^(n-3)+⋯+a^(n-1)+a^n (0)

= nx^(n-1)+a(n-1) x^(n-2)+a^2 (n-2) x^(n-3)+⋯+a^(n-1)

### Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (px+q)(r/x+s).

Let f = (px+q) x (r/x+s)

f’ = (px+q) (r/x+s)’+(r/x+s) (px+q)’

= (px+q) (rx^(-1)+s)’+(r/x+s)(p)

= (px+q)(-rx^(-2) )+(r/x+s)p

= (px+q)((-r)/x^2 )+(r/x+s)p

= (-pr)/x-qr/x^2 +pr/x+ps

= ps-qr/x^2

2. Concept of Limit: Let any function f(x) = y, is not defined at x = a, then the value of function at x = a is f(a), is meaningless. In this case the value of x can be taken nearer to a. Then the value of f(x) is calculated at that nearer value. Hence, the value of f(x) nearer to a. This limiting value of f(x) is known as limit of x.

### Can students skip chapter 12 of class 11th Maths?

No, students can’t skip chapter 12 of class 11th Maths. Chapter 12 (Limits and Derivatives) of grade 11th Math is an important chapter. Students have to study Continuity and Differentiability (chapter 5) in class 12th Maths. Chapter 12 (Limits and Derivatives) of class 11th Maths works as a base for chapter 5 Continuity and Differentiability of class 12th Maths. If students skip Chapter 12 (Limits and Derivatives) in class 11th Maths, they will face problems in Continuity and Differentiability (chapter 5) of class 12th Maths.

### Which topic’s knowledge will students gain after finishing chapter 12 of class 11 Maths?

After finishing chapter 12 of class 11th Maths, students will gain the knowledge of the following topics:

1. The intuitive idea of derivatives

2. Limits

3. Algebra of limits

4. Limits of polynomial and rational functions

5. Limits of trigonometric functions

6. Derivatives

7. Algebra of derivative of functions

8. Derivative of polynomial and trigonometric functions

### Are there any theorems in chapter 12 of class 11th Maths?

Yes, there are seven theorems in chapter 12 of class 11th Maths. All the theorems are good, simple, and important. Proofs of some theorems are short and easy. Students can easily understand the theorems and proofs of theorems.

### Is chapter 12 of class 11th Math simple to understand?

Chapter 12 of class 11th mathematics is neither simple and nor complicated. It lies in the middle of simple and hard because some parts of this chapter are easy, and some are difficult. If the student learn Limits properly the Differentiation section