Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 23

$2$

\begin{align*} \lim_{x\to \infty} \sqrt{\frac{8x^2-3}{2x^2+2 }}&=\lim_{x\to \infty} \sqrt{\frac{8x^2/x^2-3/x^2}{2x^2/x^2+2/x^2 }}\\ &=\lim_{x\to \infty} \sqrt{\frac{8-3/x^2}{2+2/x^2 }}\\ &=\sqrt{\frac{\lim_{x\to \infty}(8)-\lim_{x\to \infty}(3/x^2)}{\lim_{x\to \infty}(2)+\lim_{x\to \infty}(2/x^2) }}\\ &=\sqrt{\frac{8-0}{2+0 }}\\ &=2 \end{align*}