RD Sharma Class 12 Chapter 9 Solutions (Continuity)
RD Sharma Class 12 Maths Solutions for Chapter 9 Continuity are designed for students who will appear in CBSE and several other competitive examinations. These solutions help you to acquire the concepts and apply them to solve problems of various difficulty levels. These RD Sharma Solutions also help in accurately explaining the notion of continuity, continuity at a point, algebra of continuous functions, continuity on types of intervals, definition and meaning of types of continuous functions, and properties of continuous functions.
The solutions provided in RD Sharma for Class 12 Maths Chapter 9 – Continuity consist of 33 questions in two exercises. These questions are based on various topics explained in the Continuity chapter. The solutions are arranged in the same manner as they are arranged in the RD Sharma Class 12 Maths book. The solutions listed here will assist you in understanding the type of questions asked in CBSE as well as the other competitive exams such as JEE Main & JEE Advanced.
Practising Solutions from RD Sharma Class 12 Maths can help you score good grades in the CBSE Board exams. You will see solutions are explained in a simple, easy to understand language. They are written by highly experienced subject matter experts who have extensive knowledge of the subjects. Upon practising these solutions, you will be ready to answer complex continuity problems.
Topics Covered in RD Sharma Class 12 Maths Solutions for Chapter 9 Continuity
Algebra of continuous functions: In Algebra of continuous functions, you’ll learn the rules of addition, subtraction, multiplication and division that relate to the continuity of functions. They are as follows:
Given f(x) and g(x), the two continuous functions found at the point x = a. If the above is true, we get the following rules:
- The Addition Rule
F(x) + g(x) will be continuous at x = a
- The Subtraction Rule
F(x) – g(x) will be continuous at x = a
- The Multiplication Rule
F(x) x g(x) will be continuous at x = a
- The Division Rule
F(x)/g(x) will be continuous at x = a; given g(a) ≠ 0
Functions that are continuous everywhere – In this topic, you’ll learn about all the functions that are found continuous everywhere –
- Rational functions are found continuous over their domain, excluding the values that make the denominator = 0
- Polynomial functions are found continuous everywhere
- Absolute Value Functions are found continuous everywhere
- Sine and cosine functions are found continuous over real numbers
- Secant, tangent, cosecant, and contingent functions are found continuous over their respective function domain.
- F(x) = n root of x is continuous for real numbers, given n is odd
- F(x) = n root of x is continuous for non-negative real numbers, given n is even
Continuity on an interval, open interval and closed interval – Here you’ll learn all the types of intervals
- F is continuous in (a,b) which is an open interval if it is found to be continuous at every point in (a,b).
- F is continuous in [a,b] which is a closed interval if it is found to be continuous if,
- F is continuous in (a,b)
- limx→a+ f(x)=f(a)
- limx→b- f(x)=f(b)
Geometrical meaning of continuity
- Function f is continuous at x = c, if no break occurs in the graph of function f at (c, f(c)).
- In an interval, f is continuous if no break occurs in the graph of f function during the entire interval.
Discussion of Exercises of RD Sharma Class 12 Maths Chapter 9
- Exercise 9.1 of Continuity helps the student find if a given function is continuous or discontinuous. On solving this exercise, you will learn the methodology to prove continuity or discontinuity of a given function at a given point. This exercise teaches the elementary concept of continuity which forms a strong foundation to solve advanced problems asked in competitive exams. This exercise comprises a total of 23 questions.
- Exercise 9.2 of Continuity will help you advance to a level where you would be able to solve more difficult questions. It will make you familiar with using the basics of the topic to solve complex problems. This exercise comprises a total of 9 questions.
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