If $\lim\limits_{x\to \infty}\big(1+\large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}$$=e^2$ then the value of a and b are

Question

$\begin{array}{1 1}(a)\;a\in R,b\in R&(b)\;a=1,b\in R\\(c)\;a\in R,b=2&(d)\;a=1\;and\;b=2\end{array}$