lim(x->0)((2-x)/(3-x))^1/x
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lim(x->0)((2-x)/(3-x))^1/x
lim(x->0)((2-x)/(3-x))^1/x
lim(x->0)((2-x)/(3-x))^1/x
lim(x->0)((2-x)/(3-x))^1/x =lim(x->0)exp {1/x* [ ln(2-x)-ln(3-x) ] }
x->0+ 1/x* [ ln(2-x)-ln(3-x) ] ->ln(2/3)/x->+OO exp {1/x* [ ln(2-x)-ln(3-x) ] }->+OO
x->0- 1/x* [ ln(2-x)-ln(3-x) ]->ln(2/3)/x->-OO exp {1/x* [ ln(2-x)-ln(3-x) ] }->0
故原式无极限
lim(x->0)((2-x)/(3-x))^1/x
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