Question

$\underset{x\to 1}{lim}\frac{x\sin \{x-\left[x\right]\}}{x-1}$, where [.] denotes the greatest integer function, is

• A. $0$
• B. $1$
• C. not existent
• D. non of these

Answer 1

The correct option is C not existent

For ${lim}_{x\to 1}\frac{x\sin \{x-\left[x\right]\}}{x-1}$
${lim}_{x\to 1^{+}}\frac{x\sin \{x-1\}}{x-1}=1$
But LHL ${lim}_{x\to 1^{-}}\frac{x\sin \{x-0\}}{x-1}$ does not exists