If the symbol $[[]]$ denotes the greatest integer function defined in this section, evaluate the following. $($If an answer does not exist, enter DNE.$)$

$($a$)$

Evaluate each limit$.$

$($i$)$

lim$$x$7+[[$x$]]$

$($ii$)$

lim$$x$7[[$x$]]$

$($iii$)$

lim$$x$7\mathrm{.}2[[$x$]]$