Question

高数 函数极限？

请问这题怎么做？？

Answer 1

lim(x->1) (x^2+ax+b)/sin(x^2-1) =3 (0/0)

1^2+a(1)+b=0
a+b=-1 (1)
lim(x->1) (x^2+ax+b)/sin(x^2-1) =3
lim(x->1) (x^2+ax+b)/(x^2-1) =3
lim(x->1) (x^2+ax-a-1)/(x^2-1) =3
lim(x->1) (x-1)(x+(a+1) )/[(x-1)(x+1)] =3
lim(x->1) (x+(a+1) )/(x+1) =3
[1+(a+1)]/2 =3
1+(a+1) =6
a=4
from (1)
a+b=-1
4+b=-1
b=-5
(a,b) =(4,-5)

Answer 2

当x趋近于1时，sin(x^2-1)等价于x^2-1,由于最后的极限是3，由此可得对应幂次相等可知，a=-3,b=0