![]() ![]() The same line of approach is being followed in the case of continuity as well. Then follows the precise definition of the limit. The discussion is initiated with some examples so as to give some intuitive idea about it. So in the sequence, limit comes first and it is proper to begin with some discussion about it. These two concepts are closely linked together with the involvement of the concept of limit in the definition of continuity. We deal with limits and continuity which are quite fundamental for the development of calculus. As a review, we give the definition of a function, its domain, range and its graph once again before defining the limit of a function. We have discussed a function and its graph in chapter I. So before moving towards the solution section, let us have a little concept about the subtopics involved in limits and continuity. We will also learn to identify whether the given function is continuous or discontinuous at x = a. In this chapter, we are basically going to learn about the methods of finding Limits of normal function and trigonometric functions. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License Then, the ideas of the limit of a function of three or more variables and the continuity of a function of three or more variables are very similar to the definitions given earlier for a function of two variables. The answers to these questions rely on extending the concept of a δ δ disk into more than two dimensions. How can we take a limit at a point in ℝ 3 ? ℝ 3 ? What does it mean to be continuous at a point in four dimensions? Or perhaps a function g ( x, y, z, t ) g ( x, y, z, t ) can indicate air pressure at a location ( x, y, z ) ( x, y, z ) at time t. For example, suppose we have a function f ( x, y, z ) f ( x, y, z ) that gives the temperature at a physical location ( x, y, z ) ( x, y, z ) in three dimensions. The limit of a function of three or more variables occurs readily in applications. ![]() Show that the functions f ( x, y ) = 2 x 2 y 3 + 3 f ( x, y ) = 2 x 2 y 3 + 3 and g ( x, y ) = ( 2 x 2 y 3 + 3 ) 4 g ( x, y ) = ( 2 x 2 y 3 + 3 ) 4 are continuous everywhere. Using the difference law, constant multiple law, and identity law,
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