# Limits 0/0

**Calculus**Level 4

\[ \lim _{ x\to1 }{ \frac { f( x ) }{ \sqrt { x } -1 } } =2 , \qquad \lim _{ x\to 1 }{ \left[ g( x ) (\sqrt { 5x+4 } -\sqrt { 4{ x }^{ 2 }+5 } ) \right] }=-1 \]

Let \( f(x) \) and \(g(x) \) be functions satisfying the equations above. Find \( \displaystyle \lim_{x\to1} [ f(x) g(x) ] \).