Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 26

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\begin{align*} \lim _{x \rightarrow \infty} \sqrt{\frac{x^{2}-5 x}{x^{3}+x-2}}&=\lim _{x \rightarrow \infty} \sqrt{\frac{x^{2}/x^{3}-5 x/x^{3}}{x^{3}/x^{3}+x/x^{3}-2/x^{3}}}\\ &= \lim _{x \rightarrow \infty} \sqrt{\frac{1/x -5 x^{2}}{1+1/x^{2}-2/x^{3}}}\\ &= \sqrt{\frac{\lim _{x \rightarrow \infty}(1/x) -5 \lim _{x \rightarrow \infty}(1/x^{2})}{\lim _{x \rightarrow \infty}(1)+\lim _{x \rightarrow \infty}(1/x^{2})-\lim _{x \rightarrow \infty}(2/x^{3})}}\\ &= \sqrt{\frac{0 -0}{1+0-0}}\\ &=0 \end{align*}