This is the limit 2

Calculus Level 5

\[\large{\displaystyle \lim_{x\to 0} \frac{a\sin (x)-bx+cx^{2}+x^{3}}{2x^{2} \ln (1+x)-2x^3+x^{4}}}\]

If the given limit exists and is finite for constants \(a,b,c\), then it is equal to \(\frac{d}{e}\) where \(d,e\) are coprime natural numbers.

Evaluate \(a+b+c+d+e\).

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