Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 20

$\infty$

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