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find-lim-x-0-1-sinx-1-x-e-1-x-2-1-tanx-1-x-e-1-x-2-




Question Number 28426 by abdo imad last updated on 25/Jan/18
find lim_(x→0)   (((1+sinx)^(1/x)   −e^(1−(x/2)) )/((1+tanx)^(1/x) −  e^(1−(x/2)) )) .
$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:\:−{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }{\left(\mathrm{1}+{tanx}\right)^{\frac{\mathrm{1}}{{x}}} −\:\:{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }\:. \\ $$

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