question_answer

Direction (Q. Nos. 88) 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.

\[\underset{x\to 0}{\mathop{\lim }}\,\,\left[ \frac{\sin \,x}{\tan \,x} \right],\] where \[[\cdot ]\] denotes greatest integer function, is

A)  0                                            

B)  1

C)  - 1                                         

D)  not in existence