#### Answer

$\lim\limits_{x \to 0}\sqrt (7+sec^{2}x) = \sqrt 8 = 2\sqrt {2}$

#### Work Step by Step

$\lim\limits_{x \to 0} (7+sec^{2}x)= \lim\limits_{x \to 0}7 + \lim\limits_{x \to 0}sec^{2}x = 7+ \frac{1}{cos^{2}0} = 8$
Now,
$\lim\limits_{x \to 0}\sqrt (7+sec^{2}x) = \sqrt 8 = 2\sqrt{2}$