# Maclaurin series?

**Calculus**Level 3

\[ L = \lim_{x\to0} \dfrac{e^x a^x-(a^x+e^x)+\ln{(1+x)^{e^{x}-1}} -e^x\sin{x}+\sin x(1+2e^x\sin{x})+e^x\cos{(2x)} }{e^{2x}-1} \]

Let \(a\) be a constant positive real number, find the value of \(L \).

**Clarification**: \(e\) denotes Euler's number, \(e \approx 2.71828\).