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# Concept Of Limit And Continuity Pdf

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Continuity , in mathematics , rigorous formulation of the intuitive concept of a function that varies with no abrupt breaks or jumps. A function is a relationship in which every value of an independent variable—say x —is associated with a value of a dependent variable—say y. Continuity of a function is sometimes expressed by saying that if the x -values are close together, then the y -values of the function will also be close. For close x -values, the distance between the y -values can be large even if the function has no sudden jumps. On the other hand, for any point x , points can be selected close enough to it so that the y -values of this function will be as close as desired, simply by choosing the x -values to be closer than 0.

The concept of the limit is one of the most crucial things to understand in order to prepare for calculus. A limit is a number that a function approaches as the independent variable of the function approaches a given value. In the following sections, we will more carefully define a limit, as well as give examples of limits of functions to help clarify the concept. Continuity is another far-reaching concept in calculus. A function can either be continuous or discontinuous. One easy way to test for the continuity of a function is to see whether the graph of a function can be traced with a pen without lifting the pen from the paper.

In mathematics , a limit is the value that a function or sequence "approaches" as the input or index "approaches" some value. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net , and is closely related to limit and direct limit in category theory. Suppose f is a real-valued function and c is a real number. Intuitively speaking, the expression. Indeed, the function f need not even be defined at c. Thus, f x can be made arbitrarily close to the limit of 2—just by making x sufficiently close to 1.

## JEE Main Limits, Continuity and Differentiability Limits Revision Notes

Read More. Big Ideas. Answers will vary. These questions have been designed to help you gain deep understanding of the concept of limits which is of major importance in understanding calculus concepts such as the derivative and integrals of a function. Note that substitution cannot always be used to find limits of the int function. Answers for Set 2: Limits and Continuity 1.

## Category: Limits and continuity questions and answers pdf

These topics come under the main topic, i. Limits, continuity and differentiability are some of the easiest and the most important topics of Calculus in board exams, JEE and all other engineering exams. These topics are not only important for mathematics but also have their importance in Physics and Physical Chemistry. According to the analysis done by Vedantu, questions from these topics come in the JEE exam every year.

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In mathematics , the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f x to every input x. We say that the function has a limit L at an input p, if f x gets closer and closer to L as x moves closer and closer to p. More specifically, when f is applied to any input sufficiently close to p , the output value is forced arbitrarily close to L.

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