例7求 x2+x+1 x→0 x+1 im(1++2) 解 +x+1 xx x→>x+1 11 x→>y 因为im(+_2)=0,lim(1+-+-2)≠0, x→>xx r x 1+-+ 所以mx2 0. lim 〓0 1+ × x→0 2 2 所以 lim x+x+1 x+1例7 求 . 1 1 lim 2 + + + → x x x x 解 , ) 1 1 lim( ) 1 1 lim(1 2 2 x x x x x x + + + = → → 1 1 lim 2 + + + → x x x x 因为 ) 0, 1 1 lim( 2 + = x→ x x ) 0, 1 1 lim(1 2 + +  x→ x x 所以 0, 1 1 1 1 1 lim 2 2 = + + + → x x x x x , 1 1 1 1 1 lim 2 2 =  + + + → x x x x x 所以 . 1 1 lim 2 =  + + + → x x x x