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Question: \(f(x) = \frac{x^{2} + x + 2}{x^{2} + x + 1};x \in R(1,\infty)\) =...

f(x)=x2+x+2x2+x+1;x∈R(1,∞)f(x) = \frac{x^{2} + x + 2}{x^{2} + x + 1};x \in R(1,\infty) =

A

(1,11/7)(1,11/7)

B

(1,7/3](1,7/3\rbrack

C

(1,7/5](1,7/5\rbrack

D

None of these

Answer

(1,7/3](1,7/3\rbrack

Explanation

Solution

lim⁡n→∞\lim _ { n \rightarrow \infty }

n(n+1)(2n+1)6n3\frac { \mathrm { n } ( \mathrm { n } + 1 ) ( 2 \mathrm { n } + 1 ) } { 6 \mathrm { n } ^ { 3 } }

⇒ n3[1+1/n][2+1/n]6n3\frac { \mathrm { n } ^ { 3 } [ 1 + 1 / n ] [ 2 + 1 / n ] } { 6 \mathrm { n } ^ { 3 } } = 26\frac { 2 } { 6 } = 13\frac { 1 } { 3 }