a) Let p 1 Find all extrema of f(x) nk 1 x2k subject to the constraint nk 1 xk p 1 b) Prove that for all x1, , xn R, n N, and 1 n1 2 n2 p) p)...

a By symmetry we may suppose that each x j 0 Since t p pt p1 exists for all t R and p 1 it follow ...

a) Let p > 1. Find all extrema of f(x) = nk=1 x2k subject to the constraint

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a) Let p > 1. Find all extrema of f(x) = ˆ‘nk=1 x2k subject to the constraint ˆ‘nk=1 |xk|p = 1
b) Prove that

for all x1,..., xn ˆˆ R, n ˆˆ N, and 1

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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a) Let p > 1. Find all extrema of f(x) = nk=1 x2k subject to the constraint

Question:

n1/2 n2-p)/p)

Step by Step Answer:

a By symmetry we may suppose that each x j 0 Since t p pt p1 exists for all t R and p 1 it follow...View the full answer

An Introduction to Analysis

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