Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.4 Exercises: 101


Check work for reasoning.

Work Step by Step

$f+g$ is continuous for all values of x. $\dfrac{f}{g}$ is not necessarily continuous for all values of $x$ since $g$ could be zero. Example to prove why the quotient is not necessarily continuous: Both $(x-4)$ and $(x-2)$ are continuous for all values of $x$ but $\dfrac{(x-4)}{(x-2)}$ has a discontinuity (vertical asymptote) at $x=2$ and hence it is not continuous for all values of $x.$
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