Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 23

$$\sqrt[3]{\frac{ -5 }{ 8 }}$$

Given $$\lim _{x \rightarrow \infty}\sqrt[3]{\frac{2+3x-5x^2}{1+8x^2 }}$$ Then \begin{align*} \lim _{x \rightarrow \infty}\sqrt[3]{\frac{2+3x-5x^2}{1+8x^2 }}&=\lim _{x \rightarrow \infty}\sqrt[3]{\frac{2/x^2+3 /x -5 }{1/x^2+8 }}\\ &=\sqrt[3]{\frac{0+0 -5 }{0 +8 }}\\ &=\sqrt[3]{\frac{ -5 }{ 8 }} \end{align*}