NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → ∞ ⁡ 3 x - 4 3 x + 2 x + 1 3 is equal to

Options

Ae - 1 / 3
Be - 2 / 3
Ce - 1
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 → ∞ 1 + - 6 3 x + 2 x + 1 3 = e ⁡ lim x → ∞ - 6 3 x + 2 × x + 1 3 ∵ 1 ∞ f o r m = e lim x → ∞ - 2 x - 2 3 x + 2 = e - 2 / 3 (Applying L' Hospital rule)

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