If lim x → ∞ ( 1 + x a + x 2 b ) 2 x = e 2 , then the values of a and b , are

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If $\lim _{x \rightarrow \infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2 x}=e^2$, then the values of $a$ and $b$, are

MathematicsLimitsJEE MainJEE Main 2004

Options:

A
$a \in \underline{\underline{R}}, \mathrm{~b} \in \underline{\underline{=}}$
B
$a=1, b \in \underline{R}$
C
$a \in \underline{\underline{R}}, b=2$
D
$a=1$ and $b=2$

Solution:

2668 Upvotes Verified Answer

The correct answer is:
$a=1, b \in \underline{R}$

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