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$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$

 

Solve the below limit without using the above formula,   

$\lim_{x \rightarrow 0} ({\frac{sin x}{x}})^{\frac{sin x}{x - sin x}}$

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