Question

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

• A. -2
• B. -1
• C. 0
• D. 1

Answer 1

Answer: (C)

0

Answer 2

Given that,
$f(x)=[x-3]+|x-4|$
$\therefore \displaystyle\lim _{x \rightarrow 3^{-}} f(x)=\displaystyle\lim _{x \rightarrow 3^{-}} x-3+x-4$
$=\displaystyle\lim _{h \rightarrow 0} 3-h-3+3-h-4$
$=\displaystyle\lim _{h \rightarrow 0}-h+1+h$
$=-1+1+0=0$