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NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1 Continuity and Differentiability - PDF Download

JEE Mains & Advanced

NCERT solutions for class 12 maths chapter 5 exercise 5.1 Continuity and Differentiability covers continuous functions and their algebra. These solutions contain questions based on continuity. While the algebra of continuous functions may appear difficult at first for students, but with thorough practice of questions provided in ex 5.1 class 12 maths chapter 5, students can understand the pattern of questions and find their answers without any confusion.

Our subject experts of eSaral have explained this topic in simple language to strengthen the math skills to calculate the algebra of continuous functions. You will learn the basics of continuity functions and their arithmetic operations by solving questions of NCERT solutions class 12 maths ex 5.1. Class 12 maths chapter 5 exercise 5.1 NCERT solutions have included 34 questions to determine and find the continuity of different types of functions. 

Ex 5.1 class 12 maths solutions are also made available here in PDF format. You can download this free PDF of NCERT solutions from eSaral and start your preparation for board exams. 

Topics Covered in Exercise 5.1 Class 12 Mathematics Questions

Ex 5.1 class 12 maths ch 5 is based on continuity, algebra of continuous functions. Here, you can check the detailed explanation of these topics.

1.

Continuity

  • Algebra of continuous functions

  1. Continuity

If the limit of a real-valued function equals the function's value at a given point in its domain, the function is said to be continuous at that location. If a function is continuous throughout its whole domain, it is considered continuous. 

Suppose f is a real function on a subset of the real numbers and let c be a point in the domain of f. Then f is continuous at c if 

                                $\lim _{x \rightarrow c} f(x)=f(c)$

Definition - A real function f is said to be continuous if it is continuous at every point in the domain of f

Suppose f is a function defined on a closed interval [a, b], then for f to be continuous, it needs to be continuous at every point in [a, b] including the endpoints a and b. Continuity of f at a means

                  $\lim _{x \rightarrow a^{+}} f(x)=f(a)$

and continuity of f at b means $\lim _{x \rightarrow b^{-}} f(x)=f(b)$

Observe that $\lim _{x \rightarrow a^{-}} f(x)$ and $\lim _{x \rightarrow b^{+}} f(x)$ do not make sense. As a consequence of this definition, if f is defined only at one point, it is continuous there, i.e., if the domain of f is a singleton, f is a continuous function. 

  • Algebra of continuous functions 

Here, you will be studying some algebra of continuous functions. Since continuity of a function at a point is entirely dictated by the limit of the function at that point, it is reasonable to expect results analogous to the case of limits.

Theorem 1: Suppose f and g be two real functions continuous at a real number c. Then

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

(2) f – g is continuous at x = c.

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

(4) $\left(\frac{f}{g}\right)$  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.

Tips for Solving Exercise 5.1 Class 12 Chapter 5 Continuity and Differentiability

Ex 5.1 class 12 maths chapter 5 is about continuity which you must learn to build a strong understanding of concepts to solve questions related to calculus and algebra of continuous functions. Our expert faculties of mathematics have combined some effective and useful tips for solving ex 5.1 questions.

  1. Students should practice examples and questions provided in NCERT solutions to class 12 maths chapter 5 ex 5.1 to grasp the concepts with proper understanding.

  2. All the concepts and topics related to continuity and algebra of continuous functions should be analyzed in detail to get an intensive knowledge of topics.

  3. You can also go through the NCERT solutions PDF to get the step by step solutions of questions.

Importance of Solving Ex 5.1 Class 12 Maths Chapter 5 Continuity and Differentiability 

There are numerous benefits of solving ex 5.1 class 12 maths chapter 5. Here, our experienced maths teachers of eSaral have provided some advantages which you can check below.

  1. NCERT solutions for class 12 maths exercise 5.1 describes continuity and algebra of continuous functions in detailed manner by experts of eSaral so you will get a conceptual understanding of questions with ease.

  2. The questions provided in NCERT solutions class 12 maths ex 5.1 are explained with a step by step method, this will help you to solve questions in board exams without any doubt.

  3. eSaral have provided different approaches to solve ex 5.1 questions that will help you to solve complex questions with simple methods.

  4. Practicing questions in NCERT solution class 12 maths chapter 5 will build your confidence for preparing for exams.

Frequently Asked Questions

Question 1. When is fog continuous?

Answer 1. When 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.

Question 2. What do you understand by addition and subtraction of two continuous functions?

Answer 2. When two functions are continuous at a point, then addition and subtraction of two functions are said to be continuous at the same point.

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