例4.求lim 3x3+6x+2 02x3+5x2-1 6 2 1 3+ 3+6lim+2lim3 解 3x3+6x+2 3 lim 2lim2大】 x→0X r-→0X x02x3+5x2-1x→ 2+5 1 1 2+5lim--lim 2 x x3 x→0X x→0X1 例5.求1im x2+3x+5 xx3+2x2+1 1,3 1 一十 lim+3lim+5lim 解 lim x2+3x+5 1:xx2 x→0X x-→00X1 x→0X =0 x0x3+2x2+1 21 1人 1+-+ 1+2lim+lim x-→0X x-→0X 例４．求 3 3 2 3 6 2 lim x 2 5 1 x x → x x + + + − 解 3 2 3 3 2 3 6 2 3 3 6 2 lim lim 2 5 1 5 1 2 x x x x x x x x x x → → + + + + = + − + − 2 3 3 1 1 3 6lim 2lim 3 1 1 2 2 5lim lim x x x x x x x x → → → → + + = = + − 例 5．求 2 3 2 3 5 lim x 2 1 x x → x x + + + + 解 2 3 2 3 5 lim x 2 1 x x → x x + + + + 2 3 3 1 3 5 lim 2 1 1 x x x x x x → + + = + + 2 3 3 1 1 1 lim 3lim 5lim 0 1 1 1 2lim lim x x x x x x x x x x → → → → → + + = = + +