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

Step 1 of 2

Consider the given function is,

\(\lim _{x \rightarrow \infty} \frac{4-\sqrt{x}}{2+\sqrt{x}}\)

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

\(\begin{aligned}
\lim _{x \rightarrow \infty} \frac{4-\sqrt{x}}{2+\sqrt{x}} & =\lim _{x \rightarrow \infty} \frac{\frac{4}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}}}{\frac{2}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}}} \\
& =\lim _{x \rightarrow \infty} \frac{\frac{4}{\sqrt{x}}-1}{2}+1
\end{aligned}\)