Let $f : ( 0,1 ) \rightarrow \mathbb { R }$ be the function defined as $f ( x ) = \sqrt { n }$ if $x \in \left[ \frac { 1 } { n + 1 } , \frac { 1 } { n } \right)$ where $n \in \mathbb { N }$. Let $g : ( 0,1 ) \rightarrow \mathbb { R }$ be a function such that $\int _ { x ^ { 2 } } ^ { x } \sqrt { \frac { 1 - t } { t } } d t < g ( x ) < 2 \sqrt { x }$ for all $x \in ( 0,1 )$. Then $\lim _ { x \rightarrow 0 } f ( x ) g ( x )$ (A) does NOT exist (B) is equal to 1 (C) is equal to 2 (D) is equal to 3
Let $f : ( 0,1 ) \rightarrow \mathbb { R }$ be the function defined as $f ( x ) = \sqrt { n }$ if $x \in \left[ \frac { 1 } { n + 1 } , \frac { 1 } { n } \right)$ where $n \in \mathbb { N }$. Let $g : ( 0,1 ) \rightarrow \mathbb { R }$ be a function such that $\int _ { x ^ { 2 } } ^ { x } \sqrt { \frac { 1 - t } { t } } d t < g ( x ) < 2 \sqrt { x }$ for all $x \in ( 0,1 )$. Then $\lim _ { x \rightarrow 0 } f ( x ) g ( x )$
(A) does NOT exist
(B) is equal to 1
(C) is equal to 2
(D) is equal to 3