Limit's Dilemma

Calculus Level 3

\[\large \lim_{x\to0} (1+ax+bx^2)^{2/x} = e^3 \]

If the equation above holds true for constants \(a\) and \(b\), which of the following options must be true?

Clarification: \(\mathbb R\) denote the set of all real numbers.

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