lim(x→0)((1-2x)/(1+3x)) ^(1/x)
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lim(x→0)((1-2x)/(1+3x))^(1/x)lim(x→0)((1-2x)/(1+3x))^(1/x)lim(x→0)((1-2x)/(1+3x))^(1/x)lim(x→0)(1-2x
lim(x→0)((1-2x)/(1+3x)) ^(1/x)
lim(x→0)((1-2x)/(1+3x)) ^(1/x)
lim(x→0)((1-2x)/(1+3x)) ^(1/x)
lim(x→0)(1-2x)^(1/(-2x))=e,所以 lim(x→0)(1-2x)^(1/x)=e^(-2),
lim(x→0)(1+3x)^(1/(3x))=e,所以lim(x→0)(1+3x)^(1/x)=e^3,
因此,lim(x→0)((1-2x)/(1+3x)) ^(1/x)=e^(-5).
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