NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability include all concepts and theories related to the said topic. Students will learn and understand how to implement these concepts. In addition, they will also learn the rigorous formulation of the intuitive concept of function that varies. With help from NCERT Solutions Class 12 Mathematics Chapter 5, students can understand the complex theories and the simplest way to solve the problems.
NCERT Solutions Class 12 Mathematics Chapter 5 covers essential topics such as exponential and logarithmic functions. The subtopics include continuity, differentiability, logarithmic differentiation, and mean value theorem. In addition, they will engage on the core topic of the algebra of continuous functions. The chapter carries essential formulae and helps to improve their calculation. The study material is available online on Extramarks. Extramarks study material and revision notes offer solutions for all problems and answers to the questions enlisted under the chapter.
Under Continuity and Differentiability, students will easily understand the complex theorems with help from Extramarks NCERT Solutions Class 12 Mathematics Chapter 5. Furthermore, as the solutions are built based on CBSE NCERT’s latest 2022-2023 syllabus, students can be assured that they are up-to-date and ready to tackle anything in their examination. Students can visit the Extramarks website for the latest news and updates regarding Class 12 Mathematics Chapter 5.
Key Topics Covered In NCERT Solutions for Class 12 Mathematics Chapter 5
NCERT Solutions for Class 12 Mathematics Chapter 5 Continuity and Differentiability elaborates the fundamental concepts. It includes continuity of functions, their differentiability, and their relations. In addition, the notion of the continuity of a function is applied in various concepts and theories. Thus, students may refer to NCERT Solutions Class 12 Mathematics Chapter 5 to be more thorough on various concepts under the chapter. With daily practice, students can quickly gain a deep understanding of the topic. Some of the essential topics elaborated in the chapter are mainly seen repeating in various entrance exams. It includes logarithmic differentiation, derivatives of functions, and second-order derivatives.
Key topics covered in Continuity and Differentiation include
| Exercise |
Topics |
| 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 |
5.1 Introduction
The NCERT Solutions Class 12 Mathematics Chapter 5 covers all important topics and offers step-by-step solutions. Students will get an introduction to Continuity and Differentiability. It has advanced theorems and logarithms. They will also learn the essential concepts of continuity, differentiability, and relations. Further, they can grasp the knowledge of inverse trigonometric functions.
5.2 Continuity
This section is about continuity. There are various formulaeand concepts to study and understand. The students will engage in learning algebra of continuous functions. They will also learn analogous algebraic uninterrupted functions. The continuity of a function at a point is expected to show similar results to the case of limits. With the help of NCERT Solutions Class 12 Mathematics Chapter 5, the students will learn basic definitions and theorems.
5.3 Differentiability
Differentiability includes a list of derivatives and some important theorems. It is essential to know that there are a total of three theorems that appear in competitive exams. The students will learn about the derivatives of composite, implicit, and inverse trigonometric functions. They will also get in-depth learning about derivatives of implicit function.
5.4 Exponential and Logarithmic Functions
In NCERT Solutions Class 12 Mathematics, Chapter 5 includes all important sub-topics under Exponential and Logarithmic Functions. The students will witness different classes of functions like polynomial functions, rational functions, and trigonometric functions. They will also learn about a new class of related and logarithmic functions. This exercise emphasises the exponential functions and logarithms. Several examples provided for their reference help the students grasp and understand exponential and logarithmic functions.
5.5 Logarithmic Differentiation
Students learn all essential theories in NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability. The students will learn to differentiate the specific class of functions given in the particular forms. Logarithmic Differentiation is an essential topic as it appears in entrance exams such as JEE Mains and JEE Advanced.
5.6 Derivatives of Functions in Parametric Forms
The students will learn about different concepts, the relation between two variables, and the third variables in this exercise. The NCERT Solutions Class 12 Mathematics Chapter 5 covers every problem and offers a step-by-step solution. The students will be given several examples to understand the topic better and grasp the concepts.
5.7 Second Order Derivative
The students will learn how to work with second-order derivatives and their applications in various theorems. There are more examples and solutions than theory, as this topic requires a more practical approach than a theoretical approach. These examples will help the students to get a hold of the theorems and concepts.
5.8 Mean Value Theorem
In Mean Value Theorem, students will learn the functionality of the mean value theorem and its relations to Rolle’s theorem. Various examples help the students to engage with the theorem, and it’s a core concept. The mean value theorem is slightly tricky. However, students can refer to NCERT Solutions Class 12 Mathematics Chapter 5. It provides a step-by-step solution to an example based on the mean value theorem.
In addition to the details mentioned above, the chapter also includes formulaeand a detailed explanation of the formulae. Some of the formulaeof various functions in NCERT Solutions Chapter 5 Mathematics Class 12 include
- Arithmetic of Continuous Functions: The arithmetic operations performed on continuous functions are said to be continuous. If f and g both 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.
- Logarithmic Functions: The logarithmic functions are also known as exponential functions. If the logarithmic function y = ax is equivalent, it is equivalent to the exponential equation x = ay.
Students may click here to access the NCERT Solutions for Class 12 Mathematics Chapter 5 on Extramarks.
NCERT Solutions Class 12 Mathematics Chapter 5 Exercise & Answer Solutions
NCERT Solutions Class 12 Mathematics Chapter 5 Exercise and Answer Solutions are available for students to refer for free on the Extramarks website. The material offers step-by-step solutions that help students understand how to solve problems relating to the chapter. The solution also helps students solve complex questions in a simplified manner. Students may refer to NCERT Solutions Class 12 Mathematics Chapter 5 to strengthen their basics.
Students may refer to the links below to download exercise-specific questions and solutions for NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiation:
Students can also download other NCERT Solutions for all chapters of class 12 Mathematics on the Extramarks website. In addition, students can also find study material for different classes, as mentioned below.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT Solutions Class 10
- NCERT Solutions Class 11.
Students can click on the links to refer to the study material. In addition to the study material, Extramarks also provides sample papers and a list of important questions based on past year question papers of at least a decade. All information can be accessed for free by clicking on the link mentioned above.
NCERT Exemplar Class 12 Mathematics
The NCERT Exemplar Class Mathematics is an excellent source of information. It helps the students to get a grasp on the essential and complex concepts. Furthermore, the topics present in NCERT are important as they appear in the entrance exams. Therefore, students can refer to the exemplar to score better marks. It can be referred to especially when the exams are neat, and the student is short of time. Thus, an exemplar can save time and provide the best subject knowledge.
The Chapter 5 Class 12 Mathematics exemplar books have more information and slightly complex questions. The exemplars help the students practise more and prepare them for competitive exams such as JEE Main and JEE Advanced. Extramarks understand the importance of such CBSE and NCERT resources. Thus, students can download the exemplar from the Extramarks website.
Key Features of NCERT Solutions Class 12 Mathematics Chapter 5
NCERT Solutions Class 12 Mathematics Chapter 5 offers proper solutions for every example problem. With the help of NCERT Solutions, the students can score more and get a proper understanding of complex theories. Some of the key features of NCERT Solutions Class 12 Mathematics Chapter 5 include
- Every topic in Chapter 5 Class 12 Mathematics offers an in-depth explanation that helps the students understand the concept.
- The solutions are based on the latest syllabus of the CBSE 2022-23 and aid in preparing for the examination.
- Students can expand their knowledge in the core topics and get more practice solving problems.
- The students can understand their assignments based on concepts from continuity and differentiability.
- Class 12 Mathematics Chapter 5 has some important elements that can help prepare for various competitive exams.
Students can benefit from referring to the NCERT Solutions Class 12 Mathematics Chapter 5 by clicking here.