$\text{ If }f:R\to R\text{ is defined by }f\left(x\right)=[x-3]+|x-4|\text{ the value of }\underset{x\to 3^{-}}{lim} f\left(x\right)=$

$\underset{x\to 3^{-}}{\lim }\left[x-3\right]+\left|x-4\right|$

$x\to 3^{-}\Rightarrow x<3\Rightarrow x-3<0\Rightarrow [x-3]=-1\Rightarrow x-4<0\Rightarrow |x-4|=-(x-4)$

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