求该函数的极限 (x→1)lim [ x/(x-1) -1/ln x]

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求该函数的极限 (x→1)lim [ x/(x-1) -1/ln x]
求该函数的极限 (x→1)lim [ x/(x-1) -1/ln x]

求该函数的极限 (x→1)lim [ x/(x-1) -1/ln x]
极限 (x→1)lim [ x/(x-1) -1/ln x]
=极限 (x→1)lim [ xlnx-(x-1)]/[(x-1) ln x]
=lim(x→1) [lnx+1-1]/[lnx+(x-1)/x]
=lim(x→1) [xlnx]/[xlnx+(x-1)]
=lim(x→1) (lnx+1)/(lnx+1+1)
=1/2