question_answer

Direction (Q. Nos. 87) For the existence of limit at \[x=a\] of \[y=f(x)\] it must be true that\[\underset{x\to \infty }{\mathop{\lim }}\,\,f(a+h)=\underset{h\to 0}{\mathop{\lim }}\,f(a+h)\]. Here, \[x=a\] is not the end point of the interval, \[\underset{x\to 0}{\mathop{\lim }}\,f(a-h)\] is called LHL and \[\underset{x\to 0}{\mathop{\lim }}\,f(a+h)\] is called RHL.

The value of limit \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\,[(\sin \,x)],\] where \[[\cdot ]\] denotes the greater integer function is

A)  0                                            

B)  Does not exist    

C)  - 1                         

D)  1