Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 21

$$\frac{-1}{7}$$

Given $$\lim _{t \rightarrow \infty}\frac{6-t^3}{7t^3+3 }$$ Then \begin{align*} \lim _{t \rightarrow \infty}\frac{6-t^3}{7t^3+3 }&=\lim _{t \rightarrow \infty}\frac{6/t^3-t^3/t^3}{7t^3/t^3+3 /t^3}\\ &=\lim _{t \rightarrow \infty}\frac{6/t^3-1}{7 +3 /t^3}\\ &= \frac{0-1}{7+0}\\ &=\frac{-1}{7} \end{align*}