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Question

If f1(x)=x2+10xR and fn(x)=f1(fn1(x))n2,nN, then evaluate limnfn(x)

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Solution

f1(x)=x2+10f11(x)=12
fn(x)=f1(fn1(x))f1n(x)=f11(fn1(x))f1n1(x)=f1n1(x)2
f1n(x)f1n1(x)=12
f1n(x)f1n1(x)f1n1(x)f1n2(x)f12(x)f11(x)=(12)n1f1n(x)=2nfn(x)=2nx+c
f1(x)=x2+c=x2+10c=10
fn(x)=2n+10
limxfn(x)=limx2nx+10=10

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