12M05 - Continuity and Differentiability - Types of discontinuity

Показать описание

Class 12 Mathematics – Continuity and Differentiability
We know a little about differentiation of some functions. But are all functions differentiable at all the points of their domain? Take an example of function f(x) = 1/x. This function is not defined for x=0. We know this function has negative values for negative integers and positive for positive integers. So is it differentiable at x=0? What can we say about the continuity of this function at x=0? These questions will be answered in this chapter. In this chapter, we’ll learn
1. Points of discontinuity and its conditions.
2. Different types of discontinuity.
3. Continuity in an interval and continuous function.
4. Checking continuity of standard functions.
5. First principle of derivatives.
6. Differentiability at a point.
7. Differentiability in an interval and differentiable functions.
8. Parametric and implicit differentiation.
9. Logarithmic differentiation and differentiation of inverse trigonometric functions.
10. LMVT and Rolle’s Theorem.