- #1
vandanak
- 34
- 0
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
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