The limit

Calculus Level 4

\[ \large \displaystyle\lim_{x\rightarrow 0} \dfrac {axe^x-b\log (1+x)+cxe^{-x}}{x^2\sin x}=2\]

If \(a,b\) and \(c\) are constants satisfying the equation above, find \(a+b+c\).

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