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

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## #1 2008-07-19 04:39:21

tony123
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### maximum value

Determine the maximum value of

if

Last edited by tony123 (2008-07-19 04:39:53)

## #2 2008-07-19 05:50:06

JaneFairfax
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### 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

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

## #3 2008-07-19 10:49:40

cushydom
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### 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

## #4 2008-07-21 07:26:37

JaneFairfax
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### Re: maximum value

Last edited by JaneFairfax (2008-07-21 09:16:51)

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