10. (a) Suppose f≥0 is continuous on [a, b] and [² f = 0. Prove that f = 0. rb (b) Suppose f: [a, b] →R is continuous and f = 0. fo fg = 0 for all continuous functions g. Prove that ob (c) Suppose f [a, b] → R is continuous and [" fg = 0 for all continuous functions g with the property that g(a) = g(b) = 0. Prove that f = 0.

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