If the tangent line at a point (x, y) on the curve

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 $\frac{d y}{d x}=\infty$

$\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\infty}=0$

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