(a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the maximum of f(x1,x2,...,xn) is n¹/
(a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the maximum of f(x1,x2,...,xn) is n¹/
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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Question
![Question Five
(a) Let f: RR be a function given by f(x1,x2,...,xn) = x.x²...x2, where
n
=
1. Show that the maximum of f(x1, x2,...,xn) is n²/n.
k=1
(b) Prove that the improper integral
]]
dx dy
(1 + x² + y2)3/2
-∞-∞
converges.
(c) Let D be a square with sides 0≤x≤ 2 and 0 ≤ y ≤ 2. Estimate the following
integral
If
(x + 1) dx dy
D
(Hint: Do not evaluate.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d23c93b-870e-4ad1-8eae-60e3d2381ea8%2Fc5a68ca1-72f3-423a-9add-3f1e1e4e6c3b%2F9hh4nf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question Five
(a) Let f: RR be a function given by f(x1,x2,...,xn) = x.x²...x2, where
n
=
1. Show that the maximum of f(x1, x2,...,xn) is n²/n.
k=1
(b) Prove that the improper integral
]]
dx dy
(1 + x² + y2)3/2
-∞-∞
converges.
(c) Let D be a square with sides 0≤x≤ 2 and 0 ≤ y ≤ 2. Estimate the following
integral
If
(x + 1) dx dy
D
(Hint: Do not evaluate.)
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