${lim}_{x \to 1} \frac{x^{2} - \sqrt{x}}{\sqrt{x} - 1}$

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Solution

$\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - \sqrt{x}}{\sqrt{x} - 1} (\frac{0}{0}) A p p l y L - H o s p i t a l r u l e, w e g e t = {lim}_{x \to 1} \frac{2 x - \frac{1}{2 \sqrt{x}}}{\frac{1}{2 \sqrt{x}}} = \frac{2 - \frac{1}{2}}{\frac{1}{2}} = \frac{\frac{3}{2}}{\frac{1}{2}} = 3 \end{matrix}$

Hence, this is the answer.

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