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Lebeque dominated convergence thm

  1. Dec 1, 2009 #1
    i got this question in my test i have solved it like this
    Lim n->∞∫sin(x/n)/(1+x/n)^ndx integral from 0 to infinity and sin(x/n)/(1+x/n)^n<=e^-x as sin(x/n)<=1 and (1+x/n)^n tends to e^x so we can apply dominated convergence thm as all fn(x) will be less than e^-x so taking limit inside as sin(x/n) tends to zero as n tends to infinity so answer should be 0 well I have not written detailed steps but if my questions is not clear please say it
    Is this correct or else how we have to solve it
  2. jcsd
  3. Dec 1, 2009 #2


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    Science Advisor

    Looks all right to me. Suggestion: use punctuation!!!
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