Question

If f(x) =$\frac{1}{1 - 2\cos x}$, where [x] denotes the greatest integer less than or equal to x, then $(\sqrt{\sin x})$ equals to

• A. 1
• B. 0
• C. –1
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\lim _ { x \rightarrow 0 ^ { - } } f ( x ) = \lim _ { x \rightarrow 0 ^ { - } } \frac { \sin [ x ] } { [ x ] } = \frac { \sin ( - 1 ) } { ( - 1 ) }$

= sin 1 and $\lim _ { x \rightarrow 0 ^ { + } } f ( x ) = 0$as it is given that f(x) = 0 for

[x] = 0 ⇒ $\lim _ { x \rightarrow 0 }$ f(x) doesn’t exist