Lim n -n2 n-12-n-2n2-3 n-1-A- 0B- 2 0C- 4D- -

The correct option is C 4 lim_n→ ∞ n(2n+1)^2/(n+2)(n^2 + 3n 1) = lim_n→ ∞(4n^3 + 4n^2 + n) /(n^3+5n^2 +5n 2) =lim_n→ ∞ n^3×(4 + 4/n + 1/n^2)/n^3(1+ 5/n + 5/ ...

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Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

lim n →∞n2 n+...

Question

$l i m_{n \to \infty}$ $\frac{n ((2 n + 1)^{2})}{(n + 2) (n^{2} + 3 n - 1)}$ =

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Solution

The correct option is C
4

$l i m_{n \to \infty}$ $\frac{n (2 n + 1)^{2}}{(n + 2) (n^{2} + 3 n - 1)}$
= $l i m_{n \to \infty}$ $\frac{({4 n}^{3} + {4 n}^{2} + n)}{(n^{3} + {5 n}^{2} + 5 n - 2)}$
= $l i m_{n \to \infty}$ $\frac{n^{3} \times (4 + \frac{4}{n} + \frac{1}{n^{2}})}{n^{3} (1 + \frac{5}{n} + \frac{5}{n^{2}} - \frac{2}{n^{3}})}$ =4

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lim n \to \infty \frac{n (2 n + 1)^{2}}{(n + 2) (n^{2} + 3 n - 1)}

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$l i m_{n \to \infty}$ $\frac{n ((2 n + 1)^{2})}{(n + 2) (n^{2} + 3 n - 1)}$ =

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limn→∞ n((2n+1)2)(n+2)(n2+3n−1) =

The correct option is C 4 limn→∞ n(2n+1)2(n+2)(n2+3n−1) = limn→∞(4n3+4n2+n)(n3+5n2+5n−2) =limn→∞ n3×(4+4n+1n2)n3(1+5n+5n2−2n3) =4

$l i m_{n \to \infty}$ $\frac{n ((2 n + 1)^{2})}{(n + 2) (n^{2} + 3 n - 1)}$ =