用等价无穷小替换 原式=lim(x→0)√(2sin^2(x/2))/sinx =lim(x→0)√2|sin(x/2)|/sinx 因为右极限为lim(x→0+)√2*sin(x/2)/sinx=lim(x→0)√2*(x/2)/2=√2/2 类似地,左极限为-√2/2 所以极限不存在.
