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RS Aggarwal Class 12 Chapter 9 Solutions (Continuity and Differentiability)

RS Aggarwal Solutions for Class 12 Chapter 9 Continuity and Differentiability is prepared to aid you to solve all the questions. This chapter is the fundamental chapter in the subject of calculus. In the RS Aggarwal Solutions for Class 12 Chapter – Continuity and Differentiability you will learn what a continuous function is and how continuity of a function is dependent on its domain. You will also learn how the inverse and the modulus of a continuous function is a continuous function too. 

You will be introduced to some special functions which are continuous in their respective domains such as inverse trigonometric functions, Logarithmic functions, tangent and cotangent functions, etc; and some universally continuous functions such as constant functions, identity functions, polynomials etc.

This chapter contains 25 questions in 3 exercises with a comprehensive coverage of all the topics in your syllabus. The order in which the solutions are arranged is an increasing level of difficulty, to identify the continuity and discontinuities in different kinds of functions, is checked and updated time and again. You will get a detailed analysis of all the functions.

At Instasolv, the subject matter experts have written the answers in accordance with the latest guidelines of CBSE. Solving these exercises will make you a pro in time management. These solutions are an important resource for last-minute revisions before appearing in the CBSE Class 12th board exams. The questions adhere to standards of the pattern of question paper and therefore, it is a highly recommended resource for Chapter 9 in RS Aggarwal Class 12 Solutions

Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 9 – Continuity and Differentiability

Introduction to Continuity:

In this chapter, the meaning of the term continuous is the same as we use in our daily life. If a function f(x) is said to be normal at a point x = a, it implies that the graph of the function has no holes or gaps at the given point. A real-valued function f(x) is continuous at a point ‘a’ in its domain if and only if 

i.e. the value and limit of the function at x = a are equal.

Continuity:

A function that is continuous at every point in its domain is said to be continuous.

Algebra of Continuous Functions:

  • For two real functions f and g which are continuous at x = a and α is a real number. Then,
    • f+g will be continuous at x = a.
    • f-g will be continuous at x = a.
    • αf will be continuous at x = a.
    • fg will be continuous at x = a.
    • 1/f   will be continuous at x = a, provided that f(a) ≠ 0.
    • f/g  will be continuous at x = a, provided that g(a) ≠ 0.
  • If f and g are real functions such that fog is defined and g is continuous at x = a and f is continuous at g(a), then fog is continuous at x = a.
  • The functions given below are continuous everywhere:
    1. Constant functions
    2. Identity functions
    3. Polynomial functions
    4. Modulus functions
    5. Exponential functions
    6. Sine and Cosine functions
  • The functions given below are continuous in their domain
    1. Logarithmic functions
    2. Rational functions:
    3. Tangent and cotangent functions
    4. Secant and cosecant functions
  • For a continuous function f, | f | and  1/f . are continuous in their domain
  • Sin-1 x, cos-1 x, tan-1 x, cot-1 x, cosec-1 x and sec-1 x are continuous functions in their respective domains.

Highlights of Chapter 9 ‘Continuity and Differentiability’

  • In this chapter, the meaning of continuous functions has been explained if the graphs of the functions have no breakpoints or gaps between different points for a given domain.
  • The difference between a continuous and non-continuous function can be expressed by means of graphs, hence graphs are of vital importance while studying about any function.
  • Proofs of various theorems and understanding of the behaviour of continuous functions when they are subjected to algebraic calculations can be understood by practising the solutions given ahead.
  • We will also study various corollaries extracted from these theorems and prove them.

Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 2 Functions

  1. You will learn about the conditions required to prove a function if it’s continuous or discontinuous by checking the mandatory condition in exercise solutions for 9A.
  2. In the exercise solutions for 9B, you will be required to check the continuity of more complex functions. 
  3. In the final exercise 9C, you will have to check both the continuity as well as differentiability of the given functions.
  4. The exercise questions are a rendition of the paper patterns of competitive exams, and thus will boost your analytical skills exponentially.
  5. You should solve these questions compulsorily to improve your marks in maths substantially.

Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 2 by Instasolv

  1. The answers at Instasolv are written by experts in the layman’s language in a step by step fashion to make you understand the exact algorithm.
  2. The maths team of Instasolv has curated the answers to fulfil its commitment to building strong calculus fundamentals in your understanding.
  3. At Instasolv, you will find each and every exercise question covered thoroughly.