原式=limx→0 (sin^2x-x^2cos^2x)/x^4(arcsinx~x,等价无穷小替换)
=limx→0 (sin^2x-x^2)/x^4+limx→0 (x^2-x^2cos^2x)/x^4
=limx→0 (sin2x-2x)/4x^3+limx→0 sin^2x/x^2,
=limx→0 (2cos2x-2)/12x^2+1
=limx→0 -4sin^2x/12x^2+1
=-1/3+1
=2/3.
原式=limx→0 (sin^2x-x^2cos^2x)/x^4(arcsinx~x,等价无穷小替换)
=limx→0 (sin^2x-x^2)/x^4+limx→0 (x^2-x^2cos^2x)/x^4
=limx→0 (sin2x-2x)/4x^3+limx→0 sin^2x/x^2,
=limx→0 (2cos2x-2)/12x^2+1
=limx→0 -4sin^2x/12x^2+1
=-1/3+1
=2/3.