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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → ∞ ( 3 x − 4 3 x + 2 ) x + 1 3 is equal to

Options

  1. Ae − 1 / 3
  2. Be − 2 / 3
  3. Ce − 1
  4. De − 2

Correct answer

B. e − 2 / 3

Step-by-step solution

lim x → ∞ ( 3 x − 4 3 x + 2 ) x + 1 3 = lim x → ∞ ( 3 x + 2 − 6 3 x + 2 ) x + 1 3 = lim x → ∞ ( 1 − 6 3 x + 2 ) x + 1 3 = lim x → ∞ [ ( 1 − 6 3 x + 2 ) 3 x + 2 − 6 ] − 6 3 x + 2 . x + 1 3 = lim x → ∞ e − 2 ( x + 1 ) 3 x + 2 = e − 2 / 3 , ∵ lim x → ∞ − 2 ( x + 1 ) 3 x + 2 = − 2 3 .

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