If limx→∞ 1+ax+bx22x=e2, then

# If $\underset{x\to \mathrm{\infty }}{lim} {\left(1+\frac{a}{x}+\frac{b}{{x}^{2}}\right)}^{2x}={e}^{2},$ then

1. A

$a=1,b=2$

2. B

$a=2,b=1$

3. C

$a=1,b\in R$

4. D

$a=b=1$

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### Solution:

We have,

Hence, $a=1$ and $b\in R$

$\underset{x\to a}{lim} \frac{f\left(x\right)}{g\left(x\right)}=\underset{x\to a}{lim} \frac{{f}^{\prime \prime }\left(x\right)}{{g}^{\prime \prime }\left(x\right)}$

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