Tyra

2021-02-11

Find the limits. $\underset{x\to 3\sqrt{2}}{lim}(\frac{x}{2}-\frac{1}{x})$

broliY

Skilled2021-02-12Added 97 answers

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 $(4\sqrt{\frac{2}{3}})$

Put the value of x in the above expression we get:

on simplification of above step we get:

We get a fixed value as constant. Therefore, limit exist at the given point.

Hence,the value of limit