lebeque dominated convergence thm

by vandanak
Tags: convergence, dominated, lebeque
vandanak is offline
Dec1-09, 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
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mathman is offline
Dec1-09, 04:06 PM
Sci Advisor
P: 5,942
Looks all right to me. Suggestion: use punctuation!!!

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