Answer
$2\sqrt{2}$
Work Step by Step
Note that, $\lim\limits_{x \to a}\cos x=\cos a$ for all real numbers $a$. Using this along with our limit laws, we get
$\lim\limits_{x \to 0}\sqrt{7+\sec^2 x}=\lim\limits_{x \to 0}\sqrt{7+\dfrac{1}{\cos^2 x}}=\sqrt{7+\dfrac{1}{\cos^2 0}}=\sqrt{7+\dfrac{1}{1}}=\sqrt{7+1}=\sqrt{8}=2\sqrt{2}.$
