Find the limits. lim_{xrightarrow3sqrt2}(frac{x}{2}-frac{1}{x})

We have the given expression of limit as
$f(x)=\underset{x\to 3\sqrt{2}}{lim}(\frac{x}{2}-\frac{1}{x})$
Put the value of x in the above expression we get:
$f(x)=\frac{3\sqrt{2}}{2}-\frac{1}{3\sqrt{2}}=\frac{3}{\sqrt{2}}-\frac{1}{3\sqrt{2}}$
on simplification of above step we get:
$f(x)=\frac{9-1}{3\sqrt{2}}=\frac{8}{3\sqrt{2}}=\frac{4\sqrt{2}}{3}$
$f(x)=\frac{4\sqrt{2}}{3}$
We get a fixed value as constant. Therefore, limit exist at the given point.
Hence,the value of limit $f(x)=\underset{x\to 3\sqrt{2}}{lim}(\frac{x}{2}-\frac{1}{x})$ is $(4\sqrt{\frac{2}{3}})$