Question

高数求极限lim(x趋近于正无穷）{ (x^3+3x)^1/3 - (x^2-2x)^1/2)}

Answer 1

(x^3+3x)^1/3 - (x^2-2x)^1/2)=x[(1+3/x^2)^(1/3) - (1-2/x)^(1/2)]=x[1+1/x^2+o(1/x^2) - 1 + 1/x +o(1/x)]

取极限得 1