A) 1
B) 0
C) -1
D) None of these
Correct Answer: D
Solution :
[d] As \[x\to 0-\](i.e., approaches 0 from the left), \[[x]=-1.\] \[\therefore \underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f(x)=\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\frac{1+\sin (-1)}{-1}=-1+\sin \,\,1\] Whereas, if \[x\to {{0}^{+}}\]we get \[[x]=0.\] \[\therefore f(x)=0\Rightarrow \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(x)=0\] Thus, \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\]does not exist.
You need to login to perform this action.
You will be redirected in
3 sec
