Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 28

$$\frac{ -1}{ \sqrt {6}}$$

Given $$\lim _{y \rightarrow \infty}\frac{2-y}{\sqrt {7+6y^2} } $$ Then \begin{align*} \lim _{y \rightarrow \infty}\frac{2-y}{\sqrt {7+6y^2} }&=\lim _{y \rightarrow \infty}\frac{2/y-y/y}{\sqrt {7/y^2+6y^2/y^2} } \\ &=\lim _{y \rightarrow \infty}\frac{2/y-1 }{\sqrt {7/y^2+6 } }\\ &= \frac{-1}{ \sqrt {6}}\\ &= \frac{ -1}{ \sqrt {6}} \end{align*}