$\text{ If }f:R\to R\text{ is defined by (where }\left[\right]\text{ is g.i.f) }f\left(x\right)=[x-3]+|x-4|\text{ for }x\in R$ $\text{ then }{\mathrm{Lim}}_{x\to 3^{-}}f\left(x\right)=$

$\begin{array}{l}\underset{x\to 3^{-}}{lim} [x-3]+|x-4|\\ x\to 3^{-}\Rightarrow x<3\Rightarrow x-3<0\Rightarrow [x-3]=-1\\ \Rightarrow x-4<0\Rightarrow |x-4|=-(x-4)\\ \underset{x\to 3}{lim} [x-3]+|x-4|\\ =\underset{x\to 3^{-}}{lim} -1-(x-4)\\ =\underset{x\to 3^{-}}{lim} -1-x+4\\ =-1-3+4\\ =0\end{array}$