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sindhuja P Grade: 11
        

let 'f' be a continuous function on 'R' such that


f(1/2n)=(sin(en))e-n^2+2[n]/n2+[n]+1 where [.] denotes greatest integer function. Then find the value of f(0).

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Paidepelly


f(1/2n)=(sin(en))e-n^2+2[n]/(n2+[n]+1)


for f(0) take limit n tends to infinity both side


Lt n→∞ f(1/2n)=Lt n→∞(sin(en))e-n^2+2[n]/(n2+[n]+1)


f(0)=Lt n→∞(sin(en))e-n^2+2[n]/(n2+[n]+1)


        =Lt n→∞(sin(en))e-n^2+ Lt n→∞   2[n]/(n2+[n]+1)


        =0  +Lt n→∞   2[n]/(n2+[n]+1)


let n=[n] +f wher f is fractional part of n


so f(0) =Lt n→∞   2(n-f)/(n2+n-f+1)


find limit


f(0) =2





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Badiuddin

7 years ago
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