Chapter 2 - Practice Exercises - Page 111: 30

$$\lim_{x\to\sqrt5}g(x)=\frac{1}{2}-\sqrt5$$

$$\lim_{x\to\sqrt5}\frac{1}{x+g(x)}=2$$ $$\frac{1}{\lim_{x\to\sqrt5}(x+g(x))}=2$$ $$\lim_{x\to\sqrt5}(x+g(x))=\frac{1}{2}$$ $$\sqrt5+\lim_{x\to\sqrt5}g(x)=\frac{1}{2}$$ $$\lim_{x\to\sqrt5}g(x)=\frac{1}{2}-\sqrt5$$