Question

$\underset{x\to 1}{lim}\{-x-\frac{1}{x}\},where\{.\}$ denotes the fraction part function

• A. is equal to $1$
• B. is equal to $0$
• C. Does not exist
• D. None of these

Answer 1

The correct option is B is equal to $0$

$\because {lim}_{x\to 1}\{-x-\frac{1}{x}\}$
Substitute $x=1+h$
$\Rightarrow$RHL:${lim}_{h\to 0^{+}}\{-(1+h)-\frac{1}{(1+h)}\}=\{-2.0\}=0$
Similarly,
$\Rightarrow$LHL:${lim}_{h\to 0^{-}}\{-(1-h)-\frac{1}{(1-h)}\}=\{-2.0\}=0$
And, ${lim}_{x\to 1}\{-x-\frac{1}{x}\}=\{-1.0-\frac{1}{1.0}\}=\{-2.0\}=0$
Hence option (B) is correct.