Part B: Differentiability. CBSE Class 12 Maths Notes Chapter 5 Continuity and Differentiability. Note To understand this topic, you will need to be familiar with limits, as discussed in the chapter on derivatives in Calculus Applied to the Real World. In particular the left and right hand limits do not coincide. Value of at , Since LHL = RHL = , the function is continuous at So, there is no point of discontinuity. The notion of continuity and differentiability is a pivotal concept in calculus because it directly links and connects limits and derivatives.

148 MATHEMATICS 0.001, the value of the function is 2. In Class XI, we had learnt to differentiate certain simple functions like polynomial functions and trigonometric functions.

Using the language of left and right hand limits, we may say that the left (respectively right) hand limit of f at 0 is 1 (respectively 2). CONTINUITY AND DIFFERENTIABILITY Sir Issac Newton (1642-1727) Fig 5.1. May 22, 2019 by Sastry CBSE. A differentiable function is a function whose derivative exists at each point in its domain. 3. Here, we will learn everything about Continuity and Differentiability of a function. Differentiability – The derivative of a real valued function wrt is the function and is defined as – A function is said to be differentiable if the derivative of the function exists at all points of its domain. Continuity at a Point: A function f(x) is said to be continuous at a point x = a, if Left hand limit of f(x) at(x = a) = Right hand limit of f(x) at (x = a) = Value of f(x) at (x = a) i.e. We have already learned how to prove that a function is continuous, but now we are going to expand upon our knowledge to include the idea of differentiability…

Continuity and Differentiability Class 12 Notes Maths Chapter 5. 5.1.16 Mean Value Theorem (Lagrange) Let f : [a, b] →R be a continuous function on [a,b] and differentiable on (a, b). For continuity at , LHL-RHL.

This year we'll pick up from there and learn new concepts of differentiability and continuity of functions. CONTINUITY AND DIFFERENTIABILITY 91 Geometrically Rolle’s theorem ensures that there is at least one point on the curve y = f (x) at which tangent is parallel to x-axis (abscissa of the point lying in (a, b)). Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave.