MCQ
$\lim_\limits{\text{n} \rightarrow \infty}​\frac{\text{n}(2\text{n}+1)2}{(\text{n}+2)(\text{n}2+3\text{n}−1)}$​ is equal to:
  • A
    0
  • B
    2
  • C
    4
  • D
    $ \infty$

Answer

  1. 4

Solution:

$=\lim_\limits{\text{n} \rightarrow \infty}​\frac{\text{n}(2\text{n}+1)2}{(\text{n}+2)(\text{n}2+3\text{n}−1)}$

$ = \displaystyle \lim_{\text{n}\to\infty}{\displaystyle \frac {\left(2+\Large \frac{1}{\text{n}} \right)^2}{\left(1+\Large \frac{2}{\text{n}} \right)\left(1+\Large \frac{3}{\text{n}} - \Large \frac{1}{\text{n}^2} \right)} }=\text{n}$

$ = \displaystyle \frac{(2+0)^2}{(1+0)(1+0+0)}$

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