Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 13

$$\frac{3}{2}$$

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