The correct option is D e^2/3 For such a question we use the formula, lim x → 0 #160;(1+ax)^bx = e^ab For the given question, a = 2 b = ...

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Property 7

limx→ 01+2x1/...

Question

$lim x \to 0 (1 + 2 x)^{\frac{1}{3 x}} =$

e^{2}

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e^{\frac{3}{2}}

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e^{\frac{2}{3}}

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e^{- 2}

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Solution

The correct option is D $e^{\frac{2}{3}}$
For such a question we use the formula,
$lim$ $x \to 0 {(1 + a x)}^{\frac{b}{x}} = e^{a b}$
For the given question,
$a = 2 b =$ $\frac{1}{3}$
Hence, the answer is $e^{\frac{2}{3}}$ .

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