Mathematics Limit and Continuity

If \(\displaystyle \lim_{{x \to \infty}} \left (1 + \dfrac {a}{x} - \dfrac {4}{x^{2}}\right )^{2x} = e^{3}\), then \(a\) is equal to:

1
\(\dfrac {2}{3}\)
2
\(\dfrac {3}{2}\)
3
\(2\)
4
\(\dfrac {1}{2}\)
5
3

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