# 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 $$\displaystyle \lim_{x\to1} [ f(x) g(x) ]$$.

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