Answer
$\lim\limits_{x\to7}\sec{\frac{\pi x}{6}}=-\dfrac{2\sqrt{3}}{3}.$
Work Step by Step
Using both Theorems $1.6$ and $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)):$
$\lim\limits_{x\to7}\sec{\frac{\pi x}{6}}=\sec{(\lim\limits_{x\to7}\frac{\pi x}{6})}=\sec{\frac{7\pi}{6}}=-\dfrac{2\sqrt{3}}{3}.$
