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2. Let f, g € R[a, b]. Show that f · g € R[a, b].

2. Let f, g € R[a, b]. Show that f · g € R[a, b].

Advanced Engineering Mathematics
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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For a function h and an interval I, the oscillation of h on I is defined by w(h, I) = sup |h(æ) – h(y)|- x,YEI 1. For any two bounded functions, show that w(fg,I) < sup |f| -w(g, I) + sup |g| - w(f,I). I I 2. Let f, g € R[a, b]. Show that f - g€ R[a,b].
Transcribed Image Text:For a function h and an interval I, the oscillation of h on I is defined by w(h, I) = sup |h(æ) – h(y)|- x,YEI 1. For any two bounded functions, show that w(fg,I) < sup |f| -w(g, I) + sup |g| - w(f,I). I I 2. Let f, g € R[a, b]. Show that f - g€ R[a,b].
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