Question:
If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $y$-axis, find the value of $\frac{d x}{d y}$.
Solution:
Given that the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is $\|$ to $y$-axis.
Slope of the $y$-axis $=\infty$
$\therefore$ Slope of the tangent $\frac{d y}{d x}=\infty$
$\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\infty}=0$