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let 'f' be a continuous function on 'R' such that
f(1/2n)=(sin(en))e-n^2+2[n]2 /n2+[n]+1 where [.] denotes greatest integer function. Then find the value of f(0).
Dear Paidepelly
f(1/2n)=(sin(en))e-n^2+2[n]2 /(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]2 /(n2+[n]+1)
f(0)=Lt n→∞(sin(en))e-n^2+2[n]2 /(n2+[n]+1)
=Lt n→∞(sin(en))e-n^2+ Lt n→∞ 2[n]2 /(n2+[n]+1)
=0 +Lt n→∞ 2[n]2 /(n2+[n]+1)
let n=[n] +f wher f is fractional part of n
so f(0) =Lt n→∞ 2(n-f)2 /(n2+n-f+1)
find limit
f(0) =2
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