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**Concept of Continuity and Differentiation**

Continuity and Differentiation explained in RS Aggarwal Solutions Class 12 Maths Ch 12 is one among the vital concepts for college kids for preparing for board exams. It deals with concepts just like the derivative of functions, continuity of certain points, continuity of given intervals, et al.

The continuity of a function gets the attributes of a function and its functional values. during a given domain or interval, a function is accepted as continuous if the curve has no breaking points or missing points. that’s the curve has got to be continuous at every point in its domain.

A function f(x) is claimed to be continuous at some extent x= y if it meets the subsequent three conditions.

1) f(y) is continuous if the worth of f(y) is finite

2) f(x) limx→af is continuous at the purpose if the right-hand limit is that the same as that of the left-hand limit. Therefore, R.H.S = L.H.S.

3) limx→af f(x)= f(y)

In a given interval, f(x) can only be continuous if it’s adequate to [x1, x2]. All the conditions got to be satisfied with each and each point.

In differentiation, f(x) is claimed to be differentiable at the purpose x = y if the derivative f ‘(y) exists at each point in its interval or domain.

The differentiability formula is given by

f’ (y) = f(y+h)−f(y)hf(y+h)−f(y)h

In a particular point, if a function is continuous, then the function is often differentiable at any point x=y, in its domain. However, the vice-versa might not be true in the least times.

In the given table, the derivatives of the essential trigonometric functions are explained below from the aspect of the differentiability formula:

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d/dx (sin x) → | cos x |

d/dx (cos x) → | -sin x |

d/dx (tan x)→ | sec²x |

d/dx (cot x)→ | cosec²x |

d/dx (secx)→ | sec x tan x |

d/dx (cosec x)→ | cosecx cot x |

- The meaning of continuous functions has been explained during this chapter with regard to graphs.
- The distinction between continuous and discontinuous functions is often expressed with the assistance of a graph.
- By practicing the solutions given during this chapter, one can understand the proofs of various theorems and therefore the behavior of continuous functions when these are subjected to algebraic calculations.
- Students can study several corollaries extracted from theorems and prove them.

Chapter-3 Binary Operations Solutions

Chapter-4 Inverse Trigonometric Functions Solutions

Chapter-6 Determinants Solutions

Chapter-7 Adjoint and Inverse of a Matrix Solutions

Chapter-8 System of Linear Equations Solutions

Chapter-9 Continuity and Differentiability Solutions

Chapter-10 Differentiation Solutions

Chapter-11 Applications of Derivatives Solutions

Chapter-12 Indefinite Integral Solutions

Chapter-13 Method of Integration Solutions

Chapter-14 Some Special Integrals Solutions

Chapter-15 Integration Using Partial Fractions Solutions

Chapter-16 Definite Integrals Solutions

Chapter-17 Area of Bounded Regions Solutions

Chapter-18 Differential Equations and Their Formation Solutions

Chapter-19 Differential Equations with Variable Separable Solutions

Chapter-20 Homogeneous Differential Equations Solutions

Chapter-21 Linear Differential Equations Solutions

Chapter-22 Vectors and Their Properties Solutions

Chapter-23 Scalar, or Dot, Product of Vectors Solutions

Chapter-24 Cross, or Vector, Product of Vectors Solutions

Chapter-25 Product of Three Vectors Solutions

Chapter-26 Fundamental Concepts of 3-Dimensional Geometry Solutions

Chapter-27 Straight Line in Space Solutions

Chapter-28 The Plane Solutions

Chapter-29 Probability Solutions

Chapter-30 Bayes’s Theorem and its Applications Solutions

Chapter-31 Probability Distribution Solutions

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