Class 12

Continuity and differentiability are important topics that students should know. To understand these topics in a better way, we will first see the definition of both Continuity and Differentiability. In mathematics, Continuity is the conceptual model of the intuitive idea of a curve that develops without unexpected breaks or leaps. In calculus, differentiability is a […]

Nature exhibits the quality of continuity in many ways. For example, the rivers’ water flow never stops. A person’s lifespan is marked by a constant passage of time, which means constantly growing older. The continuity of a function is a concept found in mathematics as well. It indicates that if you can write the curve

The term Continuous Variable describes the group of variables whose values are obtained by measuring something. For example, consider the case of temperature, there can be no single value of temperature. Mainly this is because of the ever-changing values of temperature. The value of temperature does not remain the same even during the course of

If a function is not continuous, it is called a discontinuous function in algebra. A discontinuous function also has a discontinuous curve, as a continuous function does. In other terms, we can state that the curve of a discontinuous function can’t be drawn with a single stroke of a pen, i.e., we must take up the

The basic concept of continuity is a crucial part of calculus. An easy way to test it is by examining whether the pen can trace the function graph without being lifted from the paper. This is a practical way to define continuity. When we go to higher levels of concepts of continuity, a more technical

Continuity is defined at a single location; a function’s limit must exist at that location; and the value of the function at that location must equal the value of the limit at that location in order for the function to be continuous at that location. Detachable discontinuities, jump discontinuities, and endless discontinuities are the three

A function is said to be continuous if it can be drawn without the need to pick up a pencil at any point in the process. A function is said to be discontinuous if this is not the case. The same is true in mathematics. A function f(x) is continuous at the point x=c if

Various components of nature display the trait of continuity. The rivers have a constant flow of water. Human life is a continual flow of time, which means you are constantly becoming older. And so forth. Similarly, in mathematics, we have the concept of function continuity. Simply put, a function is considered to be continuous if

In mathematics, a continuous function is a function that does not contain any discontinuities, which indicates that its value does not change in an unexpected way at any point. We can ensure arbitrarily small changes in a function by confining minor changes in its input to a sufficient number of minor changes. If a particular