Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 19

$$-\infty$$

Given $$\lim _{x \rightarrow \infty}\frac{7-6x^5}{ x+3 }$$ Then \begin{align*} \lim _{x \rightarrow \infty}\frac{7-6x^5}{ x+3 }&=\lim _{x \rightarrow \infty}\frac{7/x-6x^5/x}{ x/x+3/x }\\ &=\lim _{x \rightarrow \infty}\frac{7/x-6x^4}{ 1+3/x }\\ &=-\infty \end{align*}