Question

极限问题怎么解呢

Answer 1

解：根据问题的答案，a和b只能在+/-1这两个之间选择；所以要使b为确定的实数，只能选择a=1；否则，b为-∞；
这样原式=lim(x→-1)(x^3+1-3x-3)/[(x+1)(x^3+1)]
=lim(x→-1)(x+1)^2(x-2)/[(x+1)^2(x^2-x+1)]=lim(x→-1)(x-2)/(x^2-x+1)=-1=b
对比选择题与B相符，选择B。

Answer 2

如图所示

Answer 3

lim(x->-1) [1/(ax+1) - 3/(x^3+1) ] =b
lim(x->-1) [x^3-1 -3(ax+1) ]/[(ax+1).(x^3+1) ] =b
lim(x->-1) (x^3-3ax-4 )/[(ax+1).(x^3+1) ] =b (0/0)
(-1)^3 -3a(-1) -4 =0
a= 5/3
lim(x->-1) (x^3-3ax-4 )/[(ax+1).(x^3+1) ] =b
lim(x->-1) (x^3-5x-4 )/[((5/3)x+1).(x^3+1) ] =b
lim(x->-1) (x+1)(x^2-x-4) /[((5/3)x+1).(x+1)(x^2-x+1) ] =b
lim(x->-1) (x^2-x-4) /[((5/3)x+1)(x^2-x+1) ] =b
(1+1-4) /[ (-5/3 +1 ) ( 1 +1+1) ] =b
b=1
(a,b) = (5/3 ,1 )

Answer 4

如图所示