Search results
Continuity and Differentiability is one of the most important topics which help students to understand the concepts like, continuity at a point, continuity on an interval, derivative of functions and many more.
Get NCERT Solutions of Class 12 Continuity and Differentiability, Chapter 5 of NCERT Book with solutions of all NCERT Questions. The topics of this chapter include. Continuity. Checking continuity at a particular point, and over the whole domain; Checking a function is continuous using Left Hand Limit and Right Hand Limit
This chapter is essentially a continuation of our study of differentiation of functions in Class XI. We had learnt to differentiate certain functions like polynomial functions and trigonometric functions. In this chapter, we introduce the very important concepts of continuity, differentiability and relations between them.
Continuity and differentiability are complementary to each other. The function needs to be first proved for its continuity at a point, for it to be differentiable at the point. Let us learn more about the formulas, theorems, examples of continuity and differentiability.
Continuity, differentiability, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative and mean value theorem are some of the important concepts covered in the chapter.
Feb 22, 2021 · What? Simply put, differentiable means the derivative exists at every point in its domain. Consequently, the only way for the derivative to exist is if the function also exists (i.e., is continuous) on its domain. Thus, a differentiable function is also a continuous function.
Sep 28, 2023 · In Figure \(\PageIndex{4}\) we consider three functions that have a limit at \(a = 1\text{,}\) and use them to make the idea of continuity more precise. Figure \(\PageIndex{4}\) . Functions \(f\text{,}\) \(g\text{,}\) and \(h\) that demonstrate subtly different behaviors at \(a = 1\text{.}\)
