Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 18

$$\frac{5}{3}$$

Given $$\lim _{x \rightarrow \infty}\frac{5x^2+7}{3x^2-x }$$ Then \begin{align*} \lim _{x \rightarrow \infty}\frac{5x^2+7}{3x^2-x }&=\lim _{x \rightarrow \infty}\frac{5x^2/x^2+7/x^2}{3x^2/x^2-x/x^2 }\\ &=\lim _{x \rightarrow \infty}\frac{5 +7/x^2}{3 -1/x }\\ &=\frac{5+0}{3-0}\\ &=\frac{5}{3} \end{align*}