·b 10. (a) Suppose f≥ 0 is continuous on [a, b] and f = 0. Prove that f = 0. a R is continuous and To fg = 0 for all continuous functions g. Prove that (b) Suppose f: [a, b] - f = 0. (c) Suppose f [a, b] → R is continuous and L fg = 0 for all continuous functions g with the property that g(a) = g(b) = = 0. Prove that f = 0. =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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·b
10. (a) Suppose f≥ 0 is continuous on [a, b] and
f = 0. Prove that f = 0.
a
R is continuous and
To
fg = 0 for all continuous functions g. Prove that
(b) Suppose f: [a, b] -
f = 0.
(c) Suppose f [a, b] → R is continuous and
L
fg = 0 for all continuous functions g with the
property that g(a)
= g(b) =
= 0. Prove that f = 0.
=
Transcribed Image Text:·b 10. (a) Suppose f≥ 0 is continuous on [a, b] and f = 0. Prove that f = 0. a R is continuous and To fg = 0 for all continuous functions g. Prove that (b) Suppose f: [a, b] - f = 0. (c) Suppose f [a, b] → R is continuous and L fg = 0 for all continuous functions g with the property that g(a) = g(b) = = 0. Prove that f = 0. =
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