Problem 2 Let f be continuous function on [a, b). (i) Suppose that | f(x)g(x)dx = 0
Problem 2 Let f be continuous function on [a, b). (i) Suppose that | f(x)g(x)dx = 0
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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![Problem 2
Let f be continuous function on [a, b].
(i) Suppose that
| f(x)g(x)dx = 0
(*)
for every function g, where g is continuous on [a, b]. Show that f(x) = 0, Vx E [a, b].
(ii) Suppose that (*) holds when g is continuous on [a, b] and g(a) = g(b) = 0.
Show that f(x) = 0, Vx E [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38555b51-f7bb-437a-a331-1d6dd7be3349%2F7332a498-6026-474e-94e9-79e5d8e9a40d%2F3h1exmc_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2
Let f be continuous function on [a, b].
(i) Suppose that
| f(x)g(x)dx = 0
(*)
for every function g, where g is continuous on [a, b]. Show that f(x) = 0, Vx E [a, b].
(ii) Suppose that (*) holds when g is continuous on [a, b] and g(a) = g(b) = 0.
Show that f(x) = 0, Vx E [a, b].
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