Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 771: 2



Work Step by Step

Given $$ \lim _{(x, y) \rightarrow\left(\frac{4}{9}, \frac{2}{9}\right)} \frac{x}{y}$$ Since $\frac{x}{y}$ is a rational function and is continuous at $ \left(\frac{4}{9}, \frac{2}{9}\right)$, then by using substitution, we get \begin{align*} \lim _{(x, y) \rightarrow\left(\frac{4}{9}, \frac{2}{9}\right)} \frac{x}{y}&= \frac{4/9}{2/9}\\ &=\frac{4}{2}\\ &=2 \end{align*}
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