使函数y=(x-1)√x+1/(x3-1)为无穷小量的z的变化趋势是()

使函数y=(x-1)√x+1/(x³-1)为无穷小量的z的变化趋势是()
A、x→0
B、x→1
C、x→-1
D、x→+∞
【正确答案】：C
【题目解析】：lim_x→0(x-1)√x+1/(x³-1)=1 lim_x→1(x-1)√x+1/(x³+1)=lim_x→1(x-1)√x+1/(x-1)(x²+x+1)=√2/3 lim_x→-1=(x-1)√x+1/(x³-1)=0