The greatest integer function is defined by $f(x)=[x],$ the largest integer that is less than or equal to $x.$ For instance, $[5]=5,[3\mathrm{.}2]=3,[5\mathrm{.}999]=5,[-0\mathrm{.}5]=-1,[-3\mathrm{.}2]=-4.$ Evaluate the following limit if it exists:

$\underset{x17}{lim}[x]$