(1.2) The collection of functions from R to R {f, f2,** , fn} is uniformly continuous on compacta if and only if for each compact subset K of R, and for every positive number e there exists a positive number 8 such that if x and y are elements of K which differ in absolute value by less than 8, then for each i E {1,2, …,n} the function values f:(x) and f;(y) differ in absolute value by less than e.
(1.2) The collection of functions from R to R {f, f2,** , fn} is uniformly continuous on compacta if and only if for each compact subset K of R, and for every positive number e there exists a positive number 8 such that if x and y are elements of K which differ in absolute value by less than 8, then for each i E {1,2, …,n} the function values f:(x) and f;(y) differ in absolute value by less than e.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please just answer (1.2) If you can answer both i would be thankful so i can compare my answers to both problems with their solutions but i am mainly posting this for the second subpart (1.2). Thank you.
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