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

$$2$$

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*}