lim x → ∞ 1 + 2 x 3 x =, e 6, e 3, e 2, e

lim x → ∞ ( 1 + 2 x ) 3 x ⇒ lim x → ∞ e 3 x ( 1 + 2 x - 1 ) ⇒ lim x → ∞ e 3 x × 2 x ⇒ e 6

lim x → ∞ 1 + 2 x 3 x =

Question: Answered & Verified by Expert

\lim_{x \to \infty} {(1 + \frac{2}{x})}^{3 x} =

MathematicsLimitsAP EAMCETAP EAMCET 2020 (23 Sep Shift 1)

Options:

Solution:

2240 Upvotes Verified Answer

The correct answer is:

e^{6}

$\lim_{x \to \infty} (1 + \frac{2}{x})^{3 x}$

$\Rightarrow \lim_{x \to \infty} e^{3 x (1 + \frac{2}{x} - 1)}$

$\Rightarrow \lim_{x \to \infty} e^{3 x \times \frac{2}{x}}$

$\Rightarrow e^{6}$

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