Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 20

$$\infty$$

Given $$ \lim _{x\to \infty }\frac{ x+3x^2 }{4x-1}$$ Then \begin{aligned} \lim _{x\to \infty }\frac{ x+3x^2 }{4x-1}&= \lim _{x\to \infty }\frac{ \frac{x}{x }+3\frac{x^2}{x } }{4\frac{x}{x}-\frac{1}{x}} \\ &=\lim _{x\to \infty }\frac{ 1+3x }{4 -\frac{1}{x}} \\ &=\infty \end{aligned}