1x+2x+ (2)lim arctan x)nx; 3)lim( x→+∞2 x→>0 n In(--arcta lim 解(2)原式=ex→+0 n d T arctan x)I+x lim x→+∞兀 2 lIm arctan =ex>+ 1/x =已 2 (1+x2) x→)+ 1+x 2 x-++∞(1+x2)) . 1 2 arctan ) ; (3) lim( 2 (2) lim ( 1 0 ln 1 x x x x x x x n n x + + − →+ → x x x e ln arctan ) 2 ln( lim (2) − →+ 解 原式 = x x x x e 1 / 1 1 arctan ) 2 ( 1 lim 2 + − − →+ = arctan ) 2 ( 1 lim 2 x x x x e − + − →+ = 2 2 2 2 1 1 1 1 lim x x x x e + − + − − →+ = ( ) . 2 1 2 1 1 lim e e x x x = = + − →+ ( )