求limx→0{[∫0x(√(1+t)-√(1+sint))dt]/2x4}．
limx→0∫0x{[√(1+t)-√(1+sint)]dt/2x4} =limx→0{[√(1+x)-√(1+sinx)]dt/8x3}(化简) =limx→0[(x-sinx)/8x3]•limx→0{1/[√(1+x)+√(1+sinx)]}(“0/0”型) =(1/2)limx→0[(1-cosx)/24x2](等价无穷小量代换) =(1/2)limx→0[(1/2)x2/24x2]=1/96
求limx→0{[∫0x(√(1+t)-√(1+sint))dt]/2x4}．
limx→0∫0x{[√(1+t)-√(1+sint)]dt/2x4} =limx→0{[√(1+x)-√(1+sinx)]dt/8x3}(化简) =limx→0[(x-sinx)/8x3]•limx→0{1/[√(1+x)+√(1+sinx)]}(“0/0”型) =(1/2)limx→0[(1-cosx)/24x2](等价无穷小量代换) =(1/2)limx→0[(1/2)x2/24x2]=1/96
