详细过程如图rt所示……希望能帮到你解决你心中的问题
x->1
ln(1+(x-1)] ~ (x-1)
lim(x->1) ln(1+(x-1)]/(x-1)
=lim(x->1) -(x-1)/(x-1)
=-1
e^[lim(x->1) ln(1+(x-1)]/(x-1)] = e^(-1)
//
lim(x->2+) [lnx/(x-1)]e^[ 1/(x-2)]
lim(x->2+) [lnx/(x-1)] = ln2
lim(x->2+) e^[ 1/(x-2)] ->+∞
=>lim(x->2+) [lnx/(x-1)]e^[ 1/(x-2)]->+∞
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