∵lim(x->0+) (e^(1/x)+1)*arctan(1/x)/(e^(1/x)-1)=lim(x->0+) [(1+e^(-1/x))/(1-e^(-1/x))] *arctan(1/x)= 1*π/2 = π/2lim(x->0-) (e^(1/x)+1)*arctan(1/x)/(e^(1/x)-1)= 1*(-π/2)/(-1)= π/2∴lim(x->0+) (e^(...