解：lim _(xarrow 1)(dfrac (1)(x-1)-dfrac (1)(ln x))-|||-__ __

lim _(xarrow 1)(dfrac (x)(x-1)-dfrac (1)(ln x))-|||-__ __

lim _(xarrow 1)(dfrac (x)(x-1)-dfrac (1)(ln x))-|||-__ __

[题目] lim _(xarrow 1)(dfrac (x)(x-1)-dfrac (1)(ln x))

求极限 lim _(xarrow 1)(dfrac (x)(x-1)-dfrac (1)(ln x)) .

原式为：lim _(xarrow 0)(dfrac (1)({e)^x-1}-dfrac (1)(ln (1+x)))= )=原式为：

lim _(xarrow 0)(dfrac (1)(x)-dfrac (1)({e)^x-1})-|||-__；；

lim _(xarrow 0)(dfrac (1)(x)-dfrac (1)({e)^x-1}) ()-|||-__ __

lim _(xarrow 0)(dfrac (1)(x)-dfrac (1)({e)^x-1}) ()-|||-__ __

lim _(xarrow 1)dfrac ({x)^2-1}(x-1)(e)^dfrac (1{x-1)}=

求极限 lim _(xarrow 1)dfrac (ln [ cos (x-1)] )(1-sin dfrac {pi )(2)x}