Answer
$9$
Work Step by Step
$\lim\limits_{x \to 4} 3^{\sqrt {x^{2} -2x-4}} =$
$\lim\limits_{x \to 4} 3^{\sqrt {4^{2} -2(4)-4}} =$ $3^{\sqrt {16 -8-4}} =$ $3^{\sqrt {16 -12}} =$ $3^{\sqrt {4}} =$ $ 3^{2} = 9$
(We see that the function is a composite of an exponential function, square root function, and a polynomial function. We can see that $4$ is in the domain of the function and that the function is continuous at $4$. Thus the limit can be evaluated at $4$ by plugging in $x=4$.)
