Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 25


$F(x)$ is continuous on $(-\infty,\infty)$

Work Step by Step

$F(x)=\frac{2x^2-x-1}{x^2+1}$ 1) Find the domain of $F(x)$ We notice that $x^2+1\gt0$ for $\forall x\in R$ So, $x^2+1\ne0$ for $\forall x\in R$ Therefore, $\frac{2x^2-x-1}{x^2+1}$ is defined for $\forall x\in R$ In other words, the domain of $F(x)$ is $(-\infty,\infty)$ 2) Since $F(x)$ is a rational function, according to Theorem 5, $F(x)$ is continuous on its domain. Therefore, $F(x)$ is continuous on $(-\infty,\infty)$
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