If   limx→1  asinx-1+bcosx-1+4x2-1=-2,     then   a+b    is __________

Since  RHS  is   finite   quantity,   at   x→1,   numerator  must  be  0.   Therefore      0+b+4=0      b=-4Then  limx→1  asinnx-1-4cosx-1+4x2-1=-2Put   x=1+h.   Then    limh→0  asin h+41-cos hh2+h=-2or      limh→0  asin  hh+41-cos  hh2+h=-2or      a1+02=-2or       a=-4or      a+b=8