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1. (a) Suppose f≥0 is continuous on [a, b] and S f = 0. Prove that f = 0. (b) Suppose f: [a, b] → R is continuous and Tº: fg = 0 for all continuous functions g. Prove that f = 0. rb (c) Suppose f [a, b] → R is continuous and So fg = 0 for all continuous functions g with the a property that g(a) = g(b) = 0. Prove that f = 0.

1. (a) Suppose f≥0 is continuous on [a, b] and S f = 0. Prove that f = 0. (b) Suppose f: [a, b] → R is continuous and Tº: fg = 0 for all continuous functions g. Prove that f = 0. rb (c) Suppose f [a, b] → R is continuous and So fg = 0 for all continuous functions g with the a property that g(a) = g(b) = 0. Prove that f = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you just simply answer the problem. I don't need an explanation. Thank you.

1. (a) Suppose ƒ ≥ 0 is continuous on [a, b] and [ f = 0. Prove that f = 0. a fg = 0 for all continuous functions g. Prove that (b) Suppose f [a, b] → R is continuous and f = 0. a ·b = 0 for all continuous functions g with the (c) Suppose f: [a,b] → R is continuous and fg property that g(a) = g(b) = 0. Prove that f = 0.
Transcribed Image Text:1. (a) Suppose ƒ ≥ 0 is continuous on [a, b] and [ f = 0. Prove that f = 0. a fg = 0 for all continuous functions g. Prove that (b) Suppose f [a, b] → R is continuous and f = 0. a ·b = 0 for all continuous functions g with the (c) Suppose f: [a,b] → R is continuous and fg property that g(a) = g(b) = 0. Prove that f = 0.
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