Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 26

$$\sqrt {5}$$

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