NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Class XII Mathematics chapter 5 all exercises (ex. 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, and miscellaneous exercise) English Medium and Hindi Medium. All the NCERT sols are updated for academic session 2024-25 for all boards who are following class 12 NCERT Books for their course. CBSE Solutions are in the format of PDF file and Video. Videos related to Class 12 Mathematics chapter 5 all exercises are given below in Hindi and English Medium. UP Board Students also using the same NCERT textbooks as CBSE Students. So, these solutions are useful for those also in solving their doubts. Download UP Board Solutions for Class 12 Maths Chapter 5 in Hindi and English Medium. NCERT Solutions and corresponding Offline Apps are also available to free download. All the contents on this website are free to use.

NCERT Solutions for class 12 Maths chapter 5 Continuity and Differentiability all exercises with miscellaneous exercises in Hindi and English Medium free to download. Download NCERT Books for class 12 all subjects for 2024-25 based on latest CBSE Syllabus. Join the discussion forum to ask the doubts and discuss questions with the other users..

Important Terms related to Chapter 5

1. The main points of the chapter are continuous functions, algebra of continuous functions, differentiation and continuity, chain rule, rules for derivative of inverse functions, derivative of implicit function, parametric and logarithmic functions. Second order derivatives, mean value theorems (LMV) and Rolle’s Theorem.
2. Calculus (differentiability) deals with related variables and constants. In differential calculus we investigate the way in which ‘one quantity varies when the other related quantity is made to vary’. We find the rate of change (in Application of derivatives) one variable quantity relative to another variable. The relation between a function and its derivative is same as between displacement of a particle and its velocity.
3. The derivative of f(x) at x = a is represented by the slope (gradient) of the tangent to the curve y = f(x) at the point P[a, f(a)].

Let f be a real function defined in the closed interval [a, b] such that
(i) f is continuous in the closed interval [ a, b ]
(ii) f is differentiable in the open interval ( a, b )
(iii) f (a) = f (b)
Then f'(c) = 0, where c lies in (a, b).

Let f be a real valued function defined on the closed interval [a, b] such that
(a) f is continuous on [a, b], and
(b) f is differentiable in (a, b)
Then there exists a point c in the open interval (a, b) such that f ‘(c) = [f (b) – f (a)]/[b – a]