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AP EAMCET202120 Aug 2021Morning ShiftMathematicsLimitsActual

lim n → ∞ n ( 2 n + 1 ) 2 ( n + 2 ) n 2 + 3 n - 1

Options

  1. A0
  2. B2
  3. C4
  4. D∞

Correct answer

C. 4

Step-by-step solution

Given limit, lim n → ∞ n ( 2 n + 1 ) 2 ( n + 2 ) n 2 + 3 n - 1 = lim n → ∞ n · n 2 2 + 1 n 2 n 1 + 2 n n 2 1 + 3 n - 1 n 2 = ( 2 + 0 ) 2 ( 1 + 0 ) ( 1 + 0 + 0 )   ∵ n → ∞ ,   1 n → 0 . = 4

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