Introduction to NCERT Exemplar Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
Continuity and Differentiability a core topic in calculus that plays a vital role in understanding changes and rates. The NCERT Exemplar Maths Solutions for this chapter help students to explore advanced concepts of calculus with clarity and depth. The chapter begins with the concept of continuity of a function. The solutions provide a wide range of examples to show how a function can be continuous at a point or over an interval. By solving these problems, learners strengthen their skill of identifying where a function breaks or remains smooth. This understanding is the basis for studying differentiability. Differentiability is explained as the existence of a derivative of a function. The Exemplar Solutions guide students step by step in proving whether a function is differentiable at a point. The link between continuity and differentiability is also highlighted, which is crucial for solving advanced mathematical questions. The chapter also introduces important results like the chain rule, derivatives of inverse trigonometric functions, and exponential as well as logarithmic functions. Each of these is explained with worked-out examples and detailed reasoning so that learners do not rely only on memorization but also understand the logic behind formulas.
Higher-order derivatives and their applications are also included, preparing students for upcoming chapters such as applications of derivatives. The Exemplar exercises ensure that students practice diverse questions ranging from basic conceptual checks to advanced proofs. In real life, concepts of continuity and differentiability are widely used in physics, economics, engineering, and natural sciences. They help in analyzing growth, motion, and changes in various systems. Practicing from the Exemplar equips learners not only for board exams but also for competitive tests where calculus forms a major portion. By working through the class 12 NCERT Exemplar Solutions, students gain both accuracy and confidence. They learn to approach problems systematically, build logical reasoning, and apply concepts effectively. This makes the chapter a cornerstone for success in higher mathematics.