Question

If $f:R\to R$ is defined by $f\left(x\right)=[x-3]+|x-4|$ for $x\in R$, then $\underset{x\to 3}{lim}f\left(x\right)$ is equal to

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$

Answer 1

The correct option is C $0$

Given that,
$f\left(x\right)=[x-3]+|x-4|$
$\therefore \underset{x\to 3^{-}}{lim}f\left(x\right)=\underset{x\to 3^{-}}{lim}x-3+x-4$

$=\underset{h\to 0}{lim}3-h-3+3-h-4$
$=\underset{h\to 0}{lim}-h+1+h$

$=-1+1+0=0$