(a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the maximum of f(x1, 2, . n) is n¹/n. k=1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 27E
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(a) Let f: RR be a function given by f(x1,x2,...,xn) = x²₁x²x², where
'n'
n
=
1. Show that the maximum of f(x₁, x2,...,xn) is n¹/n.
k=1
(b) Prove that the improper integral
]]
dx dy
(1 + x² + y²)3/2
converges.
Transcribed Image Text:(a) Let f: RR be a function given by f(x1,x2,...,xn) = x²₁x²x², where 'n' n = 1. Show that the maximum of f(x₁, x2,...,xn) is n¹/n. k=1 (b) Prove that the improper integral ]] dx dy (1 + x² + y²)3/2 converges.
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