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:
Slope of the $y$-axis $=\infty$
$\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\infty$
$\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\infty}=0$
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