1. [10 pts] Let f e C([a, b]). Suppose that f(x)g(x) dr = 0 a for all g e C([a, b]). Prove that f(x) = 0 for all r E [a, b]. Does the conclusion hold...
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# For all g on C([a,b]) this implies g(x)=

0.Prove that f(x) = 0 for all x om [a,b]. If, f is Riemann integrable on [a,b]? 1. [10 pts] Let f e C([a, b]). Suppose that
f(x)g(x) dr = 0
a
for all g e C([a, b]). Prove that f(x) = 0 for all r E [a, b]. Does the conclusion hold if f is Riemann
integrable on [a, b]?

1) If f(x) is not zero at some point x 0 in (a, b), then there is d&gt;0 such that (x 0 -d, x 0 +d) is a subset of [a, b] and... View the full answer

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