## Calculus 8th Edition

continuous on $(-\infty, -1)\cup(-1, \infty)$.
Let f(x)=$\sin$x. It is continuous everywhere, by theorem 7 (polynomials, rational functions, root functions, trigonometric functions are continuous on their domains) Let $g(x)=x+1$, , a polynomial, continuous everywhere, by theorem 7. $h(x)=\displaystyle \frac{f(x)}{g(x)}$ has domain: $g(x)\neq 0$ $x\neq-1$ Domain= $(-\infty, -1)\cup(-1, \infty)$. It is continuous on its domain by Th.4.5 (If $f$ and $g$ are continuous, then $\displaystyle \frac{f}{g}$ is continuous on its domain.