# NCERT Solutions Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability explains the fundamental concepts of continuity of functions, their differentiability, and the relation between both of them. There are various aspects of nature that exhibit the property of continuity like the continuously flowing rivers, time in human life, and so on. Likewise, in mathematics, the notion of the continuity of a function is applied in various situations. Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave. A differentiable function is a function whose derivative exists at each point in its domain. The concept of continuity and differentiability is studied in advanced mathematics and has multiple applications in engineering, science, economics, etc. Thus, it is crucial to gain a deep understanding of this topic.

NCERT Solutions Class 12 Maths Chapter 5 is helpful in building a clear understanding of the various aspects of limits, continuity of functions, their derivatives, properties, and methods to find derivatives. Some of the important topics explained in this chapter are derivatives of the specific standard function, logarithmic differentiation, derivatives of functions in parametric forms, and second-order derivatives. With the regular practice of Class 12 Maths NCERT Solutions Chapter 5, students will quickly gain a deep understanding of this topic. To learn and practice with NCERT Solutions Chapter 5 Continuity and Differentiability, download the exercises provided in the links below.

- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.1
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.2
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.3
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.4
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.5
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.6
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.7
- NCERT Solutions Class 12 Maths Chapter 5 Ex 5.8
- NCERT Solutions Class 12 Maths Chapter 5 Miscellaneous Exercise

## NCERT Solutions for Class 12 Maths Chapter 5 PDF

NCERT Solutions for Class 12 Maths Chapter 5 are meticulously formulated guides that promote the fundamental understanding of the representation of continuity and differentiability of functions along with their applications. To practice with these solutions, click on the links of the pdf files given below.

**ā** Download Class 12 Maths NCERT Solutions Chapter 5 Continuity and Differentiability

**NCERT Class 12 Maths Chapter 5 **

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

NCERT solutions Class 12 Maths Chapter 5 Continuity and Differentiability are highly competent guides that impart the foundational knowledge of calculus. These reliable learning resources deliver a clear sense of geometric interpretation of continuity and the differentiability of functions. The pattern followed by these solutions is quite amiable for performing a deep study of all topics. To practice the exercise-wise NCERT Solutions Class 12 Maths Continuity and Differentiability, try the exercise-wise links given below.

- Class 12 Maths Chapter 5 Ex 5.1 - 34 Questions
- Class 12 Maths Chapter 5 Ex 5.2 - 10 Questions
- Class 12 Maths Chapter 5 Ex 5.3 - 15 Questions
- Class 12 Maths Chapter 5 Ex 5.4 - 10 Questions
- Class 12 Maths Chapter 5 Ex 5.5 - 18 Questions
- Class 12 Maths Chapter 5 Ex 5.6 - 11 Questions
- Class 12 Maths Chapter 5 Ex 5.7 - 17 Questions
- Class 12 Maths Chapter 5 Ex 5.8 - 6 Questions
- Class 12 Maths Chapter 5 Miscellaneous Ex - 23 Questions

ā Download CBSE Class 12 Maths Chapter 5 NCERT Book

**Topics Covered:** The main topics covered in NCERT Solutions Class 12 Maths Chapter 5 are continuity, differentiability, exponential, logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative, and mean value theorem. Each of these topics is elaborated efficiently with interactive illustrations to help students grasp them better.

**Total Questions:** Class 12 Maths Chapter 5 Continuity and Differentiability has 144 questions in 9 exercises which are mostly short answer type questions. The sums provided in each exercise of these solutions competently cover all important topics from an exam point of view.

## List of Formulas in NCERT Solutions Class 12 Maths Chapter 5

Continuity and Differentiability are the basic topics in studying calculus. Building a precise understanding of these concepts will help in learning a higher branch of mathematics called “Analysis”. To learn the continuity of functions and their derivatives it is required to have a clear knowledge of important theorems, definitions, formulas, and rules. NCERT Solutions Class 12 Maths Chapter 5 elaborates each of them with the help of examples. Some of the important terms and formulas explained in these NCERT Solutions for Class 12 Maths Chapter 5 are given below.

**Continuous Function:**A function is said to be a continuous function if it is continuous on the whole of its domain. A continuous function f(x) is continuous on a given interval if it is continuous at every point of the interval.

**Arithmetic of Continuous Functions:**The result of arithmetic operations performed on continuous functions is continuous. i.e., if f and g are continuous functions, then

(f ± g) (x) = f(x) ± g(x) is continuous.

(f . g) (x) = f(x) . g (x) is continuous.

( f / g ) (x) = f(x ) / g(x) (wherever g(x) ≠ 0) is continuous.

**Differentiable:**A function is said to be differentiable if the derivative of the function exists at all points in its domain. Particularly, if a function f(x) is differentiable at x = a, then f′(a) exists in the domain. Some derivative rules used to find the derivatives of a function are:

i) ( f ± g )′ = f′ ± g′

ii) ( fg )′ = f′g +f g′

iii) ( f/g )′ = (f′g−fg′) /g^{2}

**Logarithmic functions**: Logarithmic functions are the inverses of exponential functions. The logarithmic function y = log_{a}x is defined to be equivalent to the exponential equation x = a^{y}.

## FAQs on NCERT Solutions for Class 12 Maths Chapter 5

### What is the Importance of NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability?

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability are highly reliable resources that provide accurate knowledge of all topics included in this chapter. A strategic study of these resources will enable students to grasp all complex concepts easily. These well-framed guides are prominent in enhancing the mathematical quotient of students to score well in annual exams. They are also a promising tool to build self-confidence for various competitive exams.

### What are the Important Topics Covered in NCERT Solutions Class 12 Maths Chapter 5?

Chapter 5 Continuity and Differentiability of class 12 Maths precisely describes all necessary concepts of continuity and differentiability of functions. The important topics covered in the NCERT Solutions Class 12 Maths Chapter 5 are continuity of functions, algebra of continuous functions, differentiability, Exponential and Logarithmic Functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative, and mean value theorem. The problems provided in these solutions are pretty efficient in delivering the fundamentals related to the above-mentioned topics. These purposefully created solutions are excellent to improve the math proficiency of students in an easy way.

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Continuity and Differentiability?

Practicing all the questions included in NCERT Solutions Class 12 Maths Continuity and Differentiability gives a step-by-step knowledge of each topic. The gradually paced problems in these solutions will assist students to simply adapt to the rising complexity level with ease. Students can go through the detailed solution of each question to build the fundamental knowledge of basics related to the continuity and differentiability of functions. Regularly practicing with these solutions will surely prepare students to appear in competitive exams.

### How Many Questions are there in Class 12 Maths NCERT Solutions Chapter 5 Continuity and Differentiability?

Class 12 Maths Chapter 5 Continuity and Differentiability has 144 questions in 9 exercises. With the efficient practice of all the sums provided in these solutions, students can learn to accurately answer the various patterns and types of questions. They can also apply these resources to build a firm mathematical foundation for excelling in exams. The intuitive format of these solutions is reliable to gain a sound knowledge of core fundamentals.

### What are the Important Formulas in NCERT Solutions Class 12 Maths Chapter 5?

NCERT Solutions Class 12 Maths Chapter 5 mainly focuses on the Continuity of functions, their differentiability, properties, and applications. Some of the important concepts explained in these solutions are the differentiability of special functions and the theorems related to them. All these basics are covered in detail with suitable examples to enhance mathematical learnability in students. The objective of these solutions is to devise a precise skillset for mastering this topic.

### Why Should I Practice NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability?

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability is a competent learning resource that gives a deep insight into exam preparation. By solving all the problems present in this chapter, students can assess their practice and knowledge for the annual exams. It is also an easy approach for covering the entire syllabus of CBSE Class 12 Maths Chapter 5. Additionally, it is a convenient way to clear all doubts and learn complex concepts.