Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 243: 63

\[4\]

\[\frac{4x-1}{x}5\] Let \[L_1=\lim_{x\rightarrow\infty}\frac{4x-1}{x}\] \[L_1=\lim_{x\rightarrow\infty}\left(4-\frac{1}{x}\right)\] \[L_1=4-0=4\] Let \[L_2=\lim_{x\rightarrow\infty}\frac{4x^2+3x}{x^2}\] \[L_1=\lim_{x\rightarrow\infty}\left(4+\frac{3}{x}\right)\] \[L_1=4+0=4\] \[\lim_{x\rightarrow\infty}\left(4-\frac{1}{x}\right)=\lim_{x\rightarrow\infty}\frac{4x^2+3x}{x^2}\] So by using Squeeze theorem \[\lim_{x\rightarrow\infty}f(x)=4\]