Question

Find the horizontal asymptotes of √3x^2+4/5x+3

Answer 1

does the equation look like this \[\sqrt{3x ^{2}}\div5x +3\]

Answer 2

\[\lim_{x\to\infty}\frac{\sqrt{3x^2}}{5x+3}=\lim_{x\to\infty}\frac{\sqrt{x^2}\sqrt3}{5x+3}\]
\(\sqrt{x^2}=|x|=x\), since \(x\to\infty\) (x is positive).
\[\lim_{x\to\infty}\frac{\sqrt3 x}{5x+3}=\lim_{x\to\infty}\frac{\sqrt3}{5+\frac{3}{x}}=\cdots\]
Do something similar for \(x\to-\infty\), with the exception that now \(\sqrt{x^2}=|x|=-x\), since x is negative.