lim(x→1)(x-x^x)/(1-x+Inx)的极限?

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lim(x→1)(x-x^x)/(1-x+Inx)的极限?lim(x→1)(x-x^x)/(1-x+Inx)的极限?lim(x→1)(x-x^x)/(1-x+Inx)的极限?lim(x→1)(x-x^

lim(x→1)(x-x^x)/(1-x+Inx)的极限?
lim(x→1)(x-x^x)/(1-x+Inx)的极限?

lim(x→1)(x-x^x)/(1-x+Inx)的极限?
lim(x→1)(x-x^x)/(1-x+Inx)
=lim(x→1)x(1-x^(x-1)/(1-x+lnx)
=lim(x→1)(1-x^(x-1))/(1-x+lnx)
=lim(x→1)(x^(x-1)(lnx+1-1/x)/(-1+1/x)
=lim(x→1)(xlnx+x-1)/(-x+1)
=lim(x→1)(lnx+1+1)/-1
=-2

用洛必达法则对分子分母同时求导化简后再使用一次洛必达法则,对分子分母求导,之后将x=1带入就行了