Continuity and Differentiability Class 12 RS Aggarwal is a crucial topic for the scholars preparing for the category 12th Board examination. The textbook provides stepwise solutions for scholars in order that they will easily solve various problems. it’ll be an excellent resource for practice and revision purposes which will level them up within the growing competitive scenario. The concepts that are a part of this chapter also seem to be helpful for future studies. the straightforward and straightforward interface of the exercise with questions and solutions makes it uncomplicated to understand the subject. Experts from the concerned discipline are involved in framing the chapter alongside an in-depth explanation. So, by following the RS Aggarwal Class 12 Maths Chapter 9 Solutions PDF by Utopper students can excel within the examination with higher grades.
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:
|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|