NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
Welcome to Myclass24's NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability. These solutions are prepared to help Class 12 students understand each problem clearly and build the confidence needed for CBSE board examinations. Whether you're revising at the last minute or studying systematically, you'll find these solutions accurate, easy to follow, and aligned with the NCERT textbook.
Summary of Chapter 5 Continuity and Differentiability
Limit, Continuity and Differentiability-Limits, Indeterminate forms, Evaluation of limit’ Hospital rule. Continuity, Definition, Differentiability: Definition, LHD, RHD, Chain rule, Differentiation of composite, Implicit, Inverse Trigonometric function, Differentiation of logarithmic, Parametric forms, Implicit, Inverse Trigonometric function, Differentiation of logarithmic, Parametric forms,2nd Order derivative, Rolle's theorem, LMVT, Examples, Functional equations and assignment discussion.
Find the PDF of NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
The PDF of NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability is available on Myclass24. Students can refer to it chapter-wise for quick revision or download it for offline use. The solutions in the PDF are written in a clear format that makes it easy to revise during exam preparation.
Chapter 5 – Continuity and Differentiability: Quick Overview
| Detail | Information |
| Chapter Number | Chapter 5 |
| Chapter Name | Continuity and Differentiability |
| Subject | Mathematics |
| Class | Class 12 |
| Board | CBSE (NCERT) |
| Total Exercises | 8 Exercises + Miscellaneous |
| Key Topics | Continuity, Differentiability, Chain Rule, Implicit Differentiation, Logarithmic, Parametric, Second Order Derivatives, Rolle's and MVT |
| Difficulty Level | High |
| Marks Weightage | Approx. 12-14 marks in board exams |
About NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
Chapter 5 is widely considered one of the most important and most challenging chapters in the entire Class 12 Maths syllabus. It carries a very high marks weightage in board exams and also forms the backbone of calculus for competitive exams. Students who invest time in this chapter consistently see a significant improvement in their overall maths scores.
The chapter begins with continuity. A function is continuous at a point if the limit of the function at that point equals the function's value there. The chapter explores continuity of composite functions, the sum, product, and quotient of continuous functions, and deals with checking continuity at points where functions are defined piecewise.
Key Concepts in Chapter 5
Differentiability comes next. A function that is differentiable at a point is also continuous there, but the converse is not always true. Students learn to test differentiability at specific points and to understand why certain functions like |x| are continuous but not differentiable at x = 0.
The chain rule for differentiation is one of the most used tools in this chapter. It allows students to differentiate composite functions, and once this is understood, topics like implicit differentiation and parametric differentiation follow naturally. Implicit differentiation involves finding dy/dx when y is not expressed explicitly in terms of x, and this is a very common board exam question type.
Differentiation of exponential and logarithmic functions is covered thoroughly. The technique of logarithmic differentiation is introduced for functions like x^x or complicated products and quotients, where direct differentiation would be very messy. This is an area where students often lose marks due to algebraic errors, and Myclass24 solutions provide clean, step-by-step working.
Inverse trigonometric functions from Chapter 2 reappear here in the context of differentiation. Derivatives like d/dx[sin⁻¹(x)] = 1/√(1-x²) need to be memorised and applied. The chapter also covers second-order derivatives and concludes with two important theorems: Rolle's Theorem and the Mean Value Theorem (MVT).
Exercise-wise Overview
This chapter has eight exercises plus a miscellaneous exercise.
Exercise 5.1 (34 questions) deals with continuity.
Exercises 5.2 to 5.6 progressively cover differentiability, the chain rule, implicit, exponential, logarithmic, and parametric differentiation.
Exercise 5.7 covers second-order derivatives.
Exercise 5.8 has questions on Rolle's and MVT.
The Miscellaneous Exercise contains 23 problems combining all the methods from the chapter.
Given the breadth and difficulty of this chapter, having reliable NCERT solutions is essential. Myclass24 solutions for Chapter 5 are crafted to match the exact level of detail expected in CBSE board exams, helping students understand not just the 'how' but also the 'why' behind each differentiation technique.