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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