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Study these definitions and prove or disprove the claims. (In all cases, n ? N.) Definition. f(n)??ifforanyC>0,thereisnC suchthatforalln?nC,f(n)?C.Definition. f(n)?aifforany?>0,thereisn?...

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Advance Math

Study these definitions and prove or disprove the claims. (Inall cases, n ? N.)

Definition. f(n)??ifforanyC>0,thereisnCsuchthatforalln?nC,f(n)?C.Definition.f(n)?aifforany?>0,thereisn? suchthatforalln?n?,|f(n)?a|??.

(a) f(n)=(2n2 +3)/(n+1). (i)f(n)??. (ii)f(n)?1. (iii)f(n)?2.

(b) f(n)=(n+3)/(n+1). (i)f(n)??. (ii)f(n)?1. (iii)f(n)?2.

(c) f(n) = nsin2(1n?). (i) f(n) ? ?. (ii) f(n) ? 1. (iii) f(n) ?2.

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