Problem 2 Let f be continuous function on [a, b). (i) Suppose that | f(x)g(x)dx = 0

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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].
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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