Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.8 Continuity - 1.8 Exercises: 28


continuous on $(-\infty, -1)\cup(-1, \infty)$.

Work Step by Step

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.
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