Sinopsis
Excerpt from Functions of Three Real Variables (Reprint From American Journal of Mathematics): Thesis for the Degree of Doctor of Philosophy in the Graduate School in the University of Illinois, 1903
We must now define limiting values and limits. We say that we is a limiting value of the variable as, if there exist values of a: in every neighborhood of 900. This may also be expressed by saying that the values of a: are dense at £00. Similarly, if no, y, and z are dense, respectively, at yo, and ac, then (1130, is a limiting value of (x, y, z). In this case (x, y, 2) may approach (mo, yo, zo) in any one of three different ways, or, to use the language of geometry, the point (x, y, z) may approach the point (mo, yo, 20) in any one of three different ways.
Wirst, we may let each of the variables vary by itself, that is, we may regard any two of the variables as constant and let the third vary. Secondly, we may let two of the variables vary simultaneously while we regard the third variable as constant. Lastly, we may let all three variables vary simultaneously. These three different kinds of variation of the variables give rise to three different kinds of limits.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from Functions of Three Real Variables (Reprint From American Journal of Mathematics): Thesis for the Degree of Doctor of Philosophy in the Graduate School in the University of Illinois, 1903
We must now define limiting values and limits. We say that we is a limiting value of the variable as, if there exist values of a: in every neighborhood of 900. This may also be expressed by saying that the values of a: are dense at £00. Similarly, if no, y, and z are dense, respectively, at yo, and ac, then (1130, is a limiting value of (x, y, z). In this case (x, y, 2) may approach (mo, yo, zo) in any one of three different ways, or, to use the language of geometry, the point (x, y, z) may approach the point (mo, yo, 20) in any one of three different ways.
Wirst, we may let each of the variables vary by itself, that is, we may regard any two of the variables as constant and let the third vary. Secondly, we may let two of the variables vary simultaneously while we regard the third variable as constant. Lastly, we may let all three variables vary simultaneously. These three different kinds of variation of the variables give rise to three different kinds of limits.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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