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katia11
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Homework Statement
Prove that, if f is continuous on [a,b] and
∫ab= l f(x) l dx = zero
then f(x) = 0 for all x in [a ,b].
Homework Equations
Hint- from book-
Section 2.4 Exercise 50
Let f and g be continuous at c. Prove that if:
(a) f(c) > o, then there exists delta > o such that f(x) > 0 for all x E (c- delta, c + delta)
(b) f(c) < o, then there exists delta > o such that f(x) < 0 for all x E (c- delta, c + delta)
(c) f(c) < g(c) , then there exists delta > o such that f(x) < g(x) for all x E (c- delta, c + delta)
The Attempt at a Solution
I understand what we are trying to prove, I can visualize it, but I have NO idea what the "hint" has to do anything. I'm really not a "math person" I discovered. That is a terrible realization. I'm not just looking for the answer though, I just have no idea where to start and proofs scare me.