Let A = [0, 1] × [0, 1] C R². Suppose f : A → R is continuous on A (re (a) suprɛ[0,1] f(x, y). Prove that for all y e [0,1], there exists xy e [0, 1] s 11
Let A = [0, 1] × [0, 1] C R². Suppose f : A → R is continuous on A (re (a) suprɛ[0,1] f(x, y). Prove that for all y e [0,1], there exists xy e [0, 1] s 11
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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Please solve (a)
![#5 Let A = [0, 1] × [0, 1] C R². Suppose f: A → R is continuous on A (relative to A).
(a)
sup¤ɛ[0,1] ƒ(x, y).
(b)
on [0, 1] (relative to [0, 1]).
Prove that for all y e [0,1], there exists xy E [0, 1] such that f(xy,y)
f (x, y).
Define F : [0, 1] → R by F(y) = suppE[0.1] f(x, y). Prove that F is continuous](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2Fe2897cd4-e153-41e5-94ca-e6196912ef5a%2Fh17si8p_processed.png&w=3840&q=75)
Transcribed Image Text:#5 Let A = [0, 1] × [0, 1] C R². Suppose f: A → R is continuous on A (relative to A).
(a)
sup¤ɛ[0,1] ƒ(x, y).
(b)
on [0, 1] (relative to [0, 1]).
Prove that for all y e [0,1], there exists xy E [0, 1] such that f(xy,y)
f (x, y).
Define F : [0, 1] → R by F(y) = suppE[0.1] f(x, y). Prove that F is continuous
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