Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 83: 23

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We have \begin{align*} \lim _{x \rightarrow \infty}\frac{\sqrt{9x^4+3x+2}}{4x^3+1} &=\lim _{x \rightarrow \infty}\frac{x^3\sqrt{\frac{9}{x^2}+\frac{3}{x^5}+\frac{2}{x^6}}}{x^3(4+\frac{1}{x^3})}\\ &=\frac{ \sqrt{0+0+0}}{4+0}\\ &=0. \end{align*}