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Lebeque dominated convergence thm 
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#1
Dec109, 06:40 AM

P: 18

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
Dec109, 04:06 PM

Sci Advisor
P: 6,039

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



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