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f: R → R. be a function given by f(x₁,x2,...,xn) = x².x..., where = 1. Show that the maximum of f(x1, x2,...,xn) is n¹/.

f: R → R. be a function given by f(x₁,x2,...,xn) = x².x..., where = 1. Show that the maximum of f(x1, x2,...,xn) is n¹/.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(a) Let f: RR. be a function given by f(x₁,2,...,xn) = x.x²...x², where 72 = 1. Show that the maximum of f(x₁,x2,...,xn) is n²/. k=1 (b) Prove that the improper integral ÏÏ 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 Jf (x² (x + 1)" dx dy D (Hint: Do not evaluate.)
Transcribed Image Text:(a) Let f: RR. be a function given by f(x₁,2,...,xn) = x.x²...x², where 72 = 1. Show that the maximum of f(x₁,x2,...,xn) is n²/. k=1 (b) Prove that the improper integral ÏÏ 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 Jf (x² (x + 1)" dx dy D (Hint: Do not evaluate.)
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