Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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45

45. Let a> 0. Prove that f(X)= iS uniformly continuaus on on [a,00),
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Transcribed Image Text:45. Let a> 0. Prove that f(X)= iS uniformly continuaus on on [a,00),
So f(c1) = a. Similarly, there exists a c2 E (a, b] with f(c2) = B. %3D Definition. Let ECR and f a function with domain E. f is uniformly continuous on E if for all E> 0, there exists a 8(e) > 0 such that for all x, y E E with |x -y| < 8, |f(x) – f(y)| < e. Example. Let ECR be bounded. Then f(x) = x² is uniformly continuous on E.
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Transcribed Image Text:So f(c1) = a. Similarly, there exists a c2 E (a, b] with f(c2) = B. %3D Definition. Let ECR and f a function with domain E. f is uniformly continuous on E if for all E> 0, there exists a 8(e) > 0 such that for all x, y E E with |x -y| < 8, |f(x) – f(y)| < e. Example. Let ECR be bounded. Then f(x) = x² is uniformly continuous on E.
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