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7. Suppose f is a continuous function on [a, b] and Sf(x)g(x) dx =0 for every continuous function g. Show that f(x) = 0 on [a, b].

7. Suppose f is a continuous function on [a, b] and Sf(x)g(x) dx =0 for every continuous function g. Show that f(x) = 0 on [a, b].

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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 Supposefis a continuous function on [a, b] and J!f(x)g(x) dx = 0 for every continuous
function g. Show that f(x) = 0 on [a, b]. 

7. Suppose f is a continuous function on [a, b] and f(x)g(x) dx =0 for every continuous function g. Show that f(x)=0 on [a, b].
Transcribed Image Text:7. Suppose f is a continuous function on [a, b] and f(x)g(x) dx =0 for every continuous function g. Show that f(x)=0 on [a, b].
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