?Find the limit or show that it does not exist.\(\lim _{x \rightarrow \infty} \frac{4

Step 1 of 2

Consider the given function is,

\(\lim _{x \rightarrow \infty} \frac{4 x+3}{5 x-1}\)

Divide both the numerator and the denominator by the highest power of x of the denominator.

\(\begin{aligned}
\lim _{x \rightarrow \infty} \frac{4 x+3}{5 x-1} & =\lim _{x \rightarrow \infty} \frac{\frac{4 x+3}{x}}{\frac{5 x-1}{x}} \\
& =\lim _{x \rightarrow \infty} \frac{4+\frac{3}{x}}{5-\frac{1}{x}}
\end{aligned}\)