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RD Sharma Solutions

RD Sharma Solutions Class 12 Maths Chapter 9 - Continuity

RD Sharma Solutions Class 12 Maths Chapter 9 - Continuity

Q: 6. What are common mistakes to avoid when solving continuity problems, and how do the solutions help?

A common mistake is incorrectly calculating the Left-Hand Limit (LHL) and Right-Hand Limit (RHL) for piecewise functions or failing to equate the limit with the function's value f(c). Our RD Sharma solutions explicitly break down each component—LHL, RHL, and f(c)—helping you to build a systematic, error-free approach and reinforcing the core conditions of continuity.

Q: 8. Beyond getting the right answer, what is the main benefit of using these step-by-step solutions for Continuity?

The main benefit is mastering the logical structure of a proof. Instead of just finding an answer, you learn the systematic process of verification required in calculus. This develops a deeper conceptual understanding of why a function is continuous or not, a skill that is fundamental for the next chapter on Differentiability and all of calculus.

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RD Sharma Solutions for Class 12 Maths Chapter 9 - Continuity - Free PDF Download

Here, you’ll get a free PDF of RD Sharma Class 12 Chapter 9 Solutions. The best teachers in India have planned and prepared Solutions for the chapter, Continuity. The exercises discuss all of the important topics, and each solution provides a comprehensive description to help students better understand the concepts. These solutions are important in your preparation for all CBSE exams, including the JEE. Many exercises are covered in Chapter 9 – Continuity. For a better understanding, the answer to each question in each exercise is given along with full, step-by-step solutions. This PDF of RD Sharma Class 12 Solutions Continuity and Differentiability will be immensely useful to you in both your assignments and final examination. Download it now from the official website of Vedantu.

RD Sharma Solution of Class 12 Maths Chapter 9 mainly focuses on the concept of continuity. The solutions are prepared by our experts to have a deeper understanding of the topics covered in this chapter and the methods to solve problems in a short period.

Class 12 RD Sharma Textbook Solutions Chapter 9 - Continuity

We have provided step-by-step solutions for all exercise questions given in the pdf of Class 12 RD Sharma Chapter 9 - Continuity. All the Exercise questions with solutions in Chapter 9 - Continuity are given below:

Exercise 9.1
Exercise 9.2

Students will focus on continuity problems in this chapter, which will include questions about proving an equation is continuous when given different values of ‘x.' We'll also look at some of the functions of continuity and draw some conclusions. You'll come across reasons for various types of queries, where you'll be asked to explain why one quantity should be replaced with a different value. The PDF is designed by RD Sharma Solution experts to help you understand the chapter and excel in the exams.

Let’s have a look at the syllabus for Class 12 Maths RD Sharma Solutions Chapter 9 - Continuity.

The intuitive notion of continuity.

Continuity at a point.

Algebra of continuous function.

Checking the continuity of a function at a point where the function has the same meaning on both sides of a given point.

Testing continuity of a function at a specific point when the function has different definitions on both sides of the given point.

Finding the constant values given in the function description when it is continuous at the defined point.

On continuity of composite function.

Continuity on an interval.

Continuity on an open interval.

Continuity on a closed interval.

Definition and meaning of continuous function.

Definition and meaning of everywhere continuous function.

Properties of continuous function.

Testing continuity of a function in its domain.

Finding the values of a constant given in its definition, when a function is continuous on its domain.

Students of class 12 can use the RD Sharma Solutions for Class 12 Chapter 9 - Continuity in the right manner that will be most beneficial for them to score good marks in the exam. This study material is created by subject experts in mathematics. These experts have worked hard day and night, to create precise study material that students of class 12 can completely rely on.

Students of class 12 CBSE who are passionate about Maths will definitely appreciate the RD Sharma book. That's because this book is one of the most in-depth books available for class 12 Maths. The most important thing that stands out and makes RD Sharma books stand out is the fact that it is through. It has the most variety of questions. The spectrum of difficulty of these questions is extremely huge. This book is extremely focused on establishing conceptualization in the students.

Benefits of Reading RD Sharma Books for Class 12

The readability of the book is extremely simple. This means that students don't have any issue with getting confused or missing a point while reading the theory part. The explanations provided for the mathematical derivations are simple and easy to grasp as well. RD Sharma explains and breaks down the NCERT textbook in the simplest and easiest manner.

Even if a student is struggling with building his foundation and doesn't know where to start, then studying the RD Sharma will help him strengthen his base. And as everyone says, consistency is the key! Well, this book helps students build a habit of studying consistently and keep the pace needed to succeed.

To download the RD Sharma Solutions for Class 12 Maths Chapter 9 - Continuity, students can click on the download button given on the same page. Students can also visit Vedantu's mobile app for more study materials.

Conclusion

Limits, Continuity, and Differentiability are the building blocks of Calculus because they are the core of the entire subject. The fundamental definition of a function's limit serves as a basis for the concepts of consistency and differentiability. These ideas are, in effect, natural extensions of the original definition. Pipes, tubes, and ducts with flowing fluids or gases, rivers, overall procedures such as diaries, power plants, highways, logistics in general, computer networks, and semiconductor technologies are some of the typical applications of the continuity equation.

FAQs on RD Sharma Solutions Class 12 Maths Chapter 9 - Continuity

1. Where can I find accurate and step-by-step RD Sharma Solutions for Class 12 Maths Chapter 9 - Continuity?

Vedantu provides comprehensive and reliable RD Sharma Solutions for Class 12 Maths Chapter 9. Our solutions are crafted by subject-matter experts and cover every question from the textbook, ensuring you get the correct method and answer for your exam preparation.

2. What is the correct method to check for a function's continuity when solving problems from RD Sharma?

To correctly solve a continuity problem as per the CBSE pattern, you must verify three key conditions at a specific point 'c':

The function f(x) must be defined at x = c, resulting in a real, finite value f(c).
The limit of the function must exist as x approaches c. This means the Left-Hand Limit (LHL) and Right-Hand Limit (RHL) must be equal.
The limit must equal the function's value: lim (x→c) f(x) = f(c).

Our solutions demonstrate this three-step verification process for every applicable problem.

3. Do the RD Sharma solutions for Chapter 9 cover all exercises and question types, like MCQs?

Yes, our RD Sharma Solutions for Class 12 Maths Chapter 9 are exhaustive. They provide detailed answers for all problems across every exercise in the chapter, including Multiple Choice Questions (MCQs), short answer questions, and long-form problems, ensuring complete preparation.

4. How do the solutions explain the continuity of complex functions like the greatest integer or modulus functions?

The solutions provide specialised, step-by-step explanations for these functions. For the greatest integer function [x] or modulus function |x|, the solutions focus on testing the continuity at critical points where the function's definition changes (e.g., at integers). They clearly show how to evaluate the LHL and RHL at these points to arrive at a definite conclusion about continuity.

5. How can using these RD Sharma solutions help me score better in my Class 12 board exams?

By following our RD Sharma solutions, you learn the precise format and step-wise logic that examiners look for. This helps you to:

Write answers that meet the CBSE marking scheme.
Understand the underlying concepts, not just memorize answers.
Gain confidence in tackling even the most challenging continuity problems.
Identify and avoid common errors in calculation and logic.

6. What are common mistakes to avoid when solving continuity problems, and how do the solutions help?

A common mistake is incorrectly calculating the Left-Hand Limit (LHL) and Right-Hand Limit (RHL) for piecewise functions or failing to equate the limit with the function's value f(c). Our RD Sharma solutions explicitly break down each component—LHL, RHL, and f(c)—helping you to build a systematic, error-free approach and reinforcing the core conditions of continuity.

7. Are the methods in these solutions aligned with the latest CBSE 2025-26 syllabus?

Absolutely. All solutions are created and verified by expert educators to be in full alignment with the latest CBSE 2025-26 syllabus and examination guidelines. The problem-solving techniques are up-to-date and reflect the standards expected in board examinations.

8. Beyond getting the right answer, what is the main benefit of using these step-by-step solutions for Continuity?

The main benefit is mastering the logical structure of a proof. Instead of just finding an answer, you learn the systematic process of verification required in calculus. This develops a deeper conceptual understanding of why a function is continuous or not, a skill that is fundamental for the next chapter on Differentiability and all of calculus.