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