x是不等式根号1-x^2>x+b在[-1,0]上恒成立,则b的取值范围是

即b<√(1-x²)-x恒成立
求出右边最小值即可
-1<=x<=0
所以令x=-sina,其中0<=a<=π/2
所以右边=√(1-sin²a)+sina
=cosa+sina
=√2sin(a+π/4)
π/4<=a+π/4<=3π/4
所以√2/2<=sin(a+π/4)<=1
1<=√2sin(a+π/4)<=√2
最小值是1
所以b<1