符合罗必塔法则,分子分母分别求导得到：
sinx^2用x^2进行等价无穷小替换.
[-(-sinx)/2√(1+cosx)]/(*2x)
=sinx/[4x√(1+cosx)]
=(sinx/x)*(1/4)*1/[√(1+cosx)]
=√2/8.
不用罗必塔法则,
极限部分
={√2-√[1+2cos^2(x/2)-1]}/x^2
=[√2-√2cos(x/2)]/x^2
=√2[1-cos(x/2)]/x^2
=√2*2*[sin(x/4)]^2/x^2
=2√2[sin(x/4)^2/[16*(x/4)^2]
=(√2/8)[sin(x/4)^2/[(x/4)^2]
=√2/8.