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Question Number 142300 by qaz last updated on 29/May/21

$$\underset{\mathrm{x}\to 0}{\lim }\frac{{({\mathrm{e}}^{\sin \mathrm{x}}+\sin \mathrm{x})}^{\frac{1}{\sin \mathrm{x}}}-{({\mathrm{e}}^{\tan \mathrm{x}}+\tan \mathrm{x})}^{\frac{1}{\tan \mathrm{x}}}}{{\mathrm{x}}^3}=?$$

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