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Boundary question

  1. May 3, 2010 #1
    show for two positive numbers x,y>0 that

    limit for n->infinity : [tex]\sqrt[n]{x^n+y^n}[/tex] = max {x,y}

    i dont know how to make a upper boundary(lower boundary is >0 i suppose)
    something like assume for instance x bigger than y and than make a boundary with it, but how?
     
    Last edited: May 3, 2010
  2. jcsd
  3. May 3, 2010 #2

    mathman

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    Science Advisor

    Assume x>y, take x outside the nth root. Use binomial theorem to show the limit of the nth root is 1.
     
  4. May 4, 2010 #3
    x^n = (x^n+y^n) = x^n(1+(y^n)/(x^n))

    =>

    nth root of (x^n+y^n)=x*nth root of (1+(y^n)/(x^n)), and for x>y, =>x. the same applies for the opposite case.
     
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