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If \[ \lim_{x\to\infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2, \] then $a=$

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For limits of the form $\left(1+\frac{f(x)}{x}\right)^{cx}$, only the coefficient of $\frac1x$ contributes to the exponent of $e$. Higher-order terms such as $\frac1{x^2}$ vanish as $x\to\infty$.

Updated On: Jul 29, 2026

$2$
$1$
$\frac{1}{2}$
$0$

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The Correct Option is B

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If \[ \lim_{x\to\infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2, \] then \(a=\)

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The Correct Option is B

Solution and Explanation

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