Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 67: 35

$\lim\limits_{x\to3}\tan{\frac{\pi x}{4}}=-1.$

Using both Theorems $1.6$ and $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)):$ $\lim\limits_{x\to3}\tan{\frac{\pi x}{4}}=\tan{(\lim\limits_{x\to3}\frac{\pi x}{4})}=\tan{\frac{3\pi}{4}}=-1.$