Continuity and Differentiability Class 12 CBSE Maths Chapter 5

Class 12 CBSE Maths Syllabus
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Applications of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11:3D Geometry
Chapter 12: Linear Programming
Chapter 13: Probability

Introduction

The important points are helpful when students are doing their revision. They can quickly refer to them to get an idea of the entire chapter without spending a lot of time on it. Below mentioned are some of the important points to be remembered from NCERT Class 12 Maths Chapter 5:

Following functions are everywhere continuous:
(a) A constant function
(b) The identity function
(c) A polynomial function
(d) Modulus function
(e) Exponential function
(f) Sine and Cosine functions
Following functions are continuous in their domains:
a) A logarithmic function
(b) A rational function
(c) Tangent, cotangent, secant and cosecant functions
(d) All inverse trigonometric functions are continuous in their respective domains
A function f(x) is said to be continuous if it is continuous at every point on its domain.
Rolle’s Theorem:
Let f be a real value of function defined on the closed interval [a, b] such that
(i) It is continuous on [a,b]
(ii) It is differentiable on (a,b) and
(iii) f(a)=f(b)
Then, there exists at least one real number c∈(a,b) such that f'(c)=0.
Lagrange’s Mean Value Theorem:
Let f(x) be a function defined on [a, b] such that
(i) It is continuous on [a,b] and
(ii) Differentiable on (a,b)
Then, there exists at least one c∈(a,b) such that f'(c)=f(b)-f(a)/b-a