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Extra Credit question

  1. May 14, 2010 #1
    So I ran into this on my multivariate calculus final this morning, I don't think anyone did it but it has been stuck in my head and I have run out of thoughts.

    Let a1, a2, …, an be n positive numbers.
    Find the maximum of [tex]\sum^{n}_{i=1}a_{i}x^_{i}[/tex]subject to the constraint [tex]\sum^{n}_{i=1}x^{2}_{i} = 1[/tex]

    Alright I've never used Latex but I believe that worked. Not quite sure, where to go looks like power sums of power 1,2.
     
    Last edited: May 14, 2010
  2. jcsd
  3. May 14, 2010 #2
  4. May 14, 2010 #3
    Yes, we studied it. About an hour ago I saw the word constraint and it popped into my head but I got discouraged when I tried to formulate it in the terms of functions. I wasn't entirely sure I could say that the summations were functions. I figure I need walk around for a moment and I will see it.
     
  5. May 16, 2010 #4
    How do you apply that to the above series though?
     
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