Study Chapter Details
UP Board Class 12 Mathematics – Continuity and Differentiability
The chapter Continuity and Differentiability is one of the most important topics in Class 12 Mathematics, forming the base for advanced calculus. It begins with the concept of continuity, which explains how a function behaves smoothly without breaks or jumps. Students learn the conditions of continuity, types of discontinuities, and continuity of various standard functions.
The chapter then moves to differentiability, which helps in determining how a function changes with respect to its variable. A key concept discussed is that every differentiable function is continuous, but the reverse is not always true. Students also study rules of differentiation, derivatives of composite, implicit, and inverse trigonometric functions.
Advanced topics such as logarithmic differentiation, exponential functions, and derivatives of functions in parametric form help strengthen problem-solving skills. The chapter plays a crucial role in understanding applications of derivatives, integrals, and higher-level mathematics. Mastering Continuity and Differentiability is essential for scoring well in UP Board exams and competitive exams like JEE.
