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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2008-07-18 06:39:21

tony123
Member
Registered: 2007-08-03
Posts: 189

maximum value

Determine the maximum value of


if

Last edited by tony123 (2008-07-18 06:39:53)

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#2 2008-07-18 07:50:06

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: maximum value

Obviously we would want

for each i for maximum. Thus, by AM–GM,

equality occurring if and only if

.

Togther with

this implies (by symmetry considerations) that
.

Hence

, and


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#3 2008-07-18 12:49:40

cushydom
Member
Registered: 2008-04-23
Posts: 10

Re: maximum value

dont know if it makes any difference but you dont need all of the sin(x) to be positive. you could have an even number of them be negative

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#4 2008-07-20 09:26:37

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: maximum value

Last edited by JaneFairfax (2008-07-20 11:16:51)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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