# NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability presents explanations to all of the questions posed in the chapter (All Exercises and Miscellaneous Exercise solutions). These Continuity and Differentiability NCERT Solutions have been expertly documented and created in accordance with the most recent CBSE Maths syllabus.

Subject experts address all of the NCERT Class 12 Maths questions. These Chapter 5 Maths Class 12 can be downloaded by students to improve their basics. Therefore we are here to provide NCERT Solutions for Class 12 Maths Chapter 5.

## Download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability PDF

Go through our Class 12 Maths Chapter 5 NCERT Solutions:

Class-12-Mathematics-Solutions-Chapter-5 pdf

Practicing these Class 12 Maths Continuity and Differentiability NCERT Solutions will aid you in the 12th board exam preparation in such a way that even the most difficult questions from this chapter will appear to be simple. Scroll down to know more!

## What will you gain in CBSE Class 12 Maths Chapter 5 – Continuity and Differentiability?

The chapter comes packed with 8 exercises along with miscellaneous exercises thus including all the essential elements associated with the topic. Let us check the subtopic covered in this chapter now-

 5.1 Introduction 5.2 Continuity 5.3 Differentiability 5.4 Exponential and Logarithmic Functions 5.5 Logarithmic Differentiation 5.6 Derivatives of Functions in Parametric Forms 5.7 Second-Order Derivative 5.8 Mean Value Theorem Others Miscellaneous Q&A

Let us now have quick look at the NCERT Solutions for Class 12 Maths Chapter 5 exercises of the chapter-

 Exercise 5.1 Solutions 34 Questions (Short Answers) Exercise 5.2 Solutions 10 Questions(Short Answers) Exercise 5.3 Solutions 15 Questions ( Short Answers) Exercise 5.4 Solutions 10 Questions (Short Answers) Exercise 5.5 Solutions 18 Questions ( Short Answers) Exercise 5.6 Solutions 11 Questions (Short Answers) Exercise 5.7 Solutions 17 Questions (Short Answers) Exercise 5.8 Solutions 6 Questions (Short Answers) Miscellaneous exercise Solutions 23 Questions (6 Long, 17 Short)

Students, let us now take a look at the content-

### NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1

With a proper introduction to the chapter, there begins the NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability. Though you have minute knowledge about the same from your previous class, however, this chapter will give complete closure to the concept.

This chapter also teaches differentiation between inverse trigonometric functions, exponential concept and logarithmic functions, robust techniques of logarithm by geometrically distinct conditions by differential calculus.

### NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2

This section teaches formula associated with the intuitive concept of functions that works without any breaks. A function is basically a relationship in which every value of the independent variable is connected with a dependable variable.

It also focuses on the algebra of continuous function, analogous algebra of uninterrupted functions,  and more. The chapter is loaded with important formulas and theories which will definitely be a need for upcoming endeavors.

### NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3

This portion lets you go through vivid details about derivatives, a list of derivatives, theorem, and formulas to follow. Additionally, this section also teaches differentiable function is continuous, derivatives of composite functions, derivatives of implicit functions, inverses trigonometric functions, chain rule of the theorem, along with various example which lets you build a clear image of the chapter.

### Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.4

This section includes the various Classes of functions, proof of the theorem, the definition of exponential functions, and logarithms. This chapter helps you build a crystal clear notion to secure solid marks from this section.

### Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.5

This section will offer knowledge that will make it simple for students to evaluate particular Classes of functions. The chapter centers around examples which simply makes it practical in its approach.

### Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.6

This section teaches about the relation between two variables which is neither implicit nor explicit. Students will be taught how to link the third variable where each of the two variables is separated by building a relationship between the first two variables. Students will also learn about the third variable and more in this section.

### Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.7

This section is also equipped with various examples to make the concept sorted thus paving your path to secure a solid understanding of the formulas and theorems enlisted here.

### Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.8

This section teaches the student how to state two fundamental results in calculus without proof,  along with theorems geometric interpretation. This section also covers the functionality of the mean value theorem and its relation to Rolle’s Theorem. The chapter also includes lots of theories and formulas associated with the content to provide an in-depth concept of the topic.

## Chapter 5 Maths Class 12 Formulas and Theorems

#### Definition of Continuity:

(i) The continuity of a real function (f) on a subset of the real numbers is defined when the function exists at point c and is given as-

lim

x→c

f(x)=f(c)

(ii) A real function (f) is said to be continuous if it is continuous at every point in the domain of f.

Consider a function f(x), and the function is said to be continuous at every point in [a, b] including the endpoints a and b.

Continuity of “f” at a means,

lim

x→a

f(x)=f(a)

Continuity of “f” at b means,

lim

x→b

f(x)=f(b)

Differentiability formula

Assume that if f is a real function and c is a point in its domain. The derivative of f at c is defined by 0

The derivative of a function f at c is defined by-

lim

h→0

f(x+h)–f(c)

h

Theorem 1: Algebra of continuous functions:

If the two real functions say f and g, are continuous at a real number c, then

(i) f + g is continuous at x=c.

(ii) f – g is continuous at x=c.

(iii) f. g is continuous at x=c.

(iv)f/g is continuous at x=c, (provided g(c) ≠ 0).

Theorem 2:  Suppose f and g are real-valued functions such that (f o g) is defined at c. If g is continuous at c and if f is continuous at g (c), then (f o g) is continuous at c.

Theorem 3: If a function f is differentiable at a point c, then it is also continuous at that point.

Theorem 4 (Chain Rule): Let f be a real-valued function which is a composite of two functions u and v; i.e., f = v o u.

Suppose t = u(x) and if both dt/dx and dv/dt exist, we have df/dx = (dv/dt). (dt/dx)

Theorem 5:

(1) The derivative of ex with respect to x is ex;  i.e., d/dx(ex) = ex.

(2) The derivative of log x with respect to x is 1/x.

i.e., d/dx(log x) =1/x.

Theorem 6 (Rolle’s Theorem): Let f : [a, b] → R be continuous on [a, b] and differentiable on (a, b), such that f(a) = f(b), where a and b are some real numbers. Then there exists some c in (a, b) such that f'(c) = 0.

## Benefits of NCERT Solutions for Class 12 Maths Chapter 5

There are several important points that ultimately support opting for this guide. Let’s check them out

1. The easy language format is undoubtedly helping you in finishing chapter 5 much before time.
2. It provides you with a thorough understanding of difficult concepts.
3. NCERT solutions follow the CBSE curriculum to a tee, and most board exam questions are drawn from them.
4. The NCERT Solutions for Class 12 Maths Chapter 5 are written by experts, there is no need to doubt the authenticity.
5. It can readily accessible and free of charge on the internet.

Well, we have jotted down the CBSE NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability in here. Make sure to get to the chapter thoroughly for securing a satisfying scorecard. Feel free to ask any queries in the comment section below!

### How many exercises are there in Chapter 5 of the NCERT textbook for Class 12 Maths?

In total, there are eight exercises in Chapter 5 of Class 12 Maths.

### Where can I get Maths Chapter 5 Class 12 NCERT solutions?

You can get NCERT Solutions for Class 12 Maths Chapter 5 from the above blog.

### Is NCERT Solutions Class 12 Maths Chapter 5 helpful?

Yes, the NCERT Ch. 5 exercises are addressed by subject matter experts who have a thorough understanding of the key ideas and every step is described in easy-to-understand language.

### Can I receive an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises?

Yes. Go through the above blog for an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises.

### Are Continuity Class 12 NCERT Solutions enough for board examinations preparation?

Yes. Continuity Class 12 NCERT Solutions covers all the topics of a matrix which is sufficient for board examinations preparation.