例1.求1imx-I 2x2-1 x-1 lim(x-1) limx-liml 解 x→2 →2 2-11 lim- x→2 x2-1 lim(x2-1)lim x2-lim1 22-13 x→2 X→2 X→2 例2.求1im x-1 1x2-1 解 x-1 lim- x-1 =lim =lim xx2-1 1(x-1)(x+1) x+1) 例3.求im 1+x-2 x→3 x-3 解 +x-2=lim (W1+x-2)W1+x+2) x-3 (x-3)(W1+x+2) x-3 1 lim- lim x3(x-3(√1+x+2)x1+x+24例１．求 2 2 1 lim x 1 x → x − − 解 2 2 2 2 2 2 2 2 2 2 lim( 1) lim lim1 1 lim 1 lim( 1) lim lim1 x x x x x x x x x x x x x → → → → → → → − − − = = − − − 2 2 1 1 2 1 3 − = = − 例２．求 2 1 1 lim x 1 x → x − − 解 2 1 1 1 1 1 1 1 lim lim lim x x x 1 ( 1)( 1) 1 2 x x → → → x x x x − − = = = − − + + 例３．求 3 1 2 lim x 3 x → x + − − 解 3 3 1 2 ( 1 2)( 1 2) lim lim 3 ( 3)( 1 2) x x x x x → → x x x + − + − + + = − − + + 3 3 3 1 1 lim lim x x ( 3)( 1 2) 1 2 4 x → → x x x − = = = − + + + +