Задача №1090

\[ \lim_{x\to{1}}\frac{x^2-\sqrt{x}}{\sqrt{x}-1} =\left[\frac{0}{0}\right] =\left[\begin{aligned}& t=\sqrt{x};\\& t\to{1}.\end{aligned}\right] =\lim_{t\to{1}}\frac{t^4-t}{t-1}=\\ =\lim_{t\to{1}}\frac{t\cdot(t-1)\cdot\left(t^2+t+1\right)}{t-1} =\lim_{t\to{1}}\left(t\cdot\left(t^2+t+1\right)\right) =3. \]