If $\left[·\right]$ denotes greatest integer function, then $\underset{x\to \frac{-3}{5}}{\lim }\frac{1}{x}\left[\frac{-1}{x}\right]=$

Given,

$\underset{x\to \frac{-3}{5}}{\lim }\frac{1}{x}\left[\frac{-1}{x}\right]$

Now putting the value of $x$ we get,

$\underset{x\to \frac{-3}{5}}{\lim }\frac{1}{x}\left[\frac{-1}{x}\right]=\frac{-5}{3}\left[\frac{5}{3}\right]=\frac{-5}{3}\times 1=\frac{-5}{3}$

As $\frac{5}{3}$ will lie between $[1,2)$ so its Greastest integer function will be $1$