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

lim_(x→0) (((e^(sin x) +sin x)^(1/(sin x)) −(e^(tan x) +tan x)^(1/(tan x)) )/x^3 )=?

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} +\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}} −\left(\mathrm{e}^{\mathrm{tan}\:\mathrm{x}} +\mathrm{tan}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{x}}} }{\mathrm{x}^{\mathrm{3}} }=? \\ $$

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