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
#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)