li(x->1)căn(x^3-x^2)/(căn(x-1)+1-x)

* Hướng dẫn giải

Chọn C.

$\begin{array}{l}\underset{x\to 1^{+}}{\lim }\frac{\sqrt{x^3-x^2}}{\sqrt{x-1}+1-x}\\ =\underset{x\to 1^{+}}{\lim }\frac{\sqrt{x^2\left(x-1\right)}}{\sqrt{x-1}-\sqrt{{\left(x-1\right)}^2}}\\ =\underset{x\to 1^{+}}{\lim }\frac{x\sqrt{x-1}}{\sqrt{x-1}\left(1-\sqrt{x-1}\right)}\\ =\underset{x\to 1^{+}}{\lim }\frac{x}{\left(1-\sqrt{x-1}\right)}=\frac{1}{1-0}=1.\end{array}$