Question

验证当x→1时(1-x^3)/(2+x)与1-x是等价无穷小

Answer 1

lim(x→1)[(1-x³)/(2+x)]/(1-x)=lim(x→1)(1-x)(1+x+x²)/[(2+x)(1-x)]

=lim(x→1)(1+x+x²)/(2+x)

=1

所以：当x→1时(1-x³)/(2+x)与1-x是等价无穷小.