RD Sharma Solutions for Class 12 Maths Chapter 9 – Continuity (Free PDF Updated for 2025–26)

RD Sharma Solutions for Class 12 Chapter 9 – Continuity are expertly crafted to help students build a strong understanding of the topic while improving their problem-solving speed and accuracy. These RD Sharma solutions are particularly beneficial for students aiming to score high marks in their board exams.

Developed by experienced subject matter experts, the solutions strictly follow the latest CBSE syllabus and exam guidelines for 2025–26. Every answer is presented step-by-step to enhance clarity and boost student confidence.

Chapter 9 focuses on the core concept of continuity in functions, providing detailed explanations, solved examples, and practical applications. Students can download the RD Sharma Solutions Class 12 Continuity PDF using the link below to reinforce their conceptual knowledge and master this important topic.

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

RD Sharma Class 12 Maths Solutions Chapter 9 – Continuity cover all the questions from the textbook, crafted by expert Mathematics teachers at Infinity Learn. Download our free PDF of Chapter 9 – Continuity RD Sharma Solutions for Class 12 to boost your performance in board exams and competitive exams.

Access the RD Sharma Solutions For Class 12 Maths Chapter 9 – Continuity

1. Test the continuity of the function at x = 0:

Function: f(x) = { x/|x|, x ≠ 0; 1, x = 0 }

• Left-hand limit (LHL): lim(x→0⁻) x/|x| = -1
• Right-hand limit (RHL): lim(x→0⁺) x/|x| = 1
• Since LHL ≠ RHL, limit doesn’t exist at x = 0
• f(0) = 1

Answer: The function is discontinuous at x = 0.

2. Show that the function is continuous at x = 3:

Function: f(x) = { (x² - x - 6)/(x - 3), x ≠ 3; 5, x = 3 }

• f(x) = (x - 3)(x + 2)/(x - 3) = x + 2 (for x ≠ 3)
• lim(x→3) f(x) = 3 + 2 = 5
• f(3) = 5

Answer: The function is continuous at x = 3.

3. Find k for continuity at x = 0:

Function: f(x) = { sin(x)/x, x ≠ 0; k, x = 0 }

• lim(x→0) sin(x)/x = 1
• f(0) = k ⇒ k = 1

Answer: Function is continuous at x = 0 when k = 1.

4. Find k for continuity at x = 0:

Function: f(x) = { (1 - cos x)/x², x ≠ 0; k, x = 0 }

• lim(x→0) (1 - cos x)/x² = ½
• k = 0.5

Answer: Function is continuous at x = 0 when k = 0.5.

5. Find k for continuity at x = 0:

Function: f(x) = { tan(x)/x, x ≠ 0; k, x = 0 }

• lim(x→0) tan(x)/x = 1
• k = 1

Answer: Function is continuous at x = 0 when k = 1.

6. Find k for continuity at x = 0:

Function: f(x) = { ln(1+x)/x, x ≠ 0; k, x = 0 }

• lim(x→0) ln(1+x)/x = 1
• k = 1

Answer: Function is continuous at x = 0 when k = 1.

7. Find k for continuity at x = 0:

Function: f(x) = { (e^x - 1)/x, x ≠ 0; k, x = 0 }

• lim(x→0) (e^x - 1)/x = 1
• k = 1

Answer: Function is continuous at x = 0 when k = 1.

8. Find k for continuity at x = 0:

Function: f(x) = { (1 - cos x)/x², x ≠ 0; k, x = 0 }

• lim(x→0) (1 - cos x)/x² = ½
• k = 0.5

Answer: Function is continuous at x = 0 when k = 0.5.

9. Find k for continuity at x = 0:

Function: f(x) = { sin(x)/x, x ≠ 0; k, x = 0 }

• lim(x→0) sin(x)/x = 1
• k = 1

Answer: Function is continuous at x = 0 when k = 1.

10. Find k for continuity at x = 0:

Function: f(x) = { tan(x)/x, x ≠ 0; k, x = 0 }

• lim(x→0) tan(x)/x = 1
• k = 1

Answer: Function is continuous at x = 0 when k = 1.

Why Use Infinity Learn RD Sharma Solutions for Continuity?

• Concept Clarity: Perfect for clearing doubts while solving exercises.
• Exam Readiness: Aligned with the latest CBSE exam pattern.
• Time-saving Resource: Helps revise complex theories quickly.
• Prepared by Experts: Solutions crafted by experienced Maths faculty.
• Boosts Confidence: Ideal for board exam practice and competitive prep.

Explore More RD Sharma Class 12 Chapter Solutions

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• Binary Operations
• Inverse Trigonometric Functions
• Algebra of Matrices
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