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let 'f' be a continuous function on 'R' such that f(1/2 n )=(sin(e n ))e -n^2 +2[n] 2 /n 2 +[n]+1 where [.] denotes greatest integer function. Then find the value of f(0).

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).

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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