In this error approximation, why can we "kill" the $\Delta x\cdot \Delta \theta$ term, but not the term with $\Delta \theta$ alone? While trying to solve a problem I've come to this equation -- where $\Delta y$ is measurement error of $y$:
$$\Delta y = \Delta h+\Delta x \cdot \tan(\theta)+x \cdot \sec^2(\theta) \cdot \Delta\theta +\Delta x \cdot \Delta\theta\sec^2(\theta)$$
The course I'm taking gets "approximate equality" by "killing" the last term because it is quadratic.
$$\Delta y \approx \Delta h+\Delta x \cdot \tan(\theta)+x \cdot \sec^2(\theta) \cdot \Delta\theta$$
My question is:

What makes the last term so different from the second-to-last that it is the one being killed, and not the former or both?


The idea here is that $\Delta x$ and $\Delta \theta$ are small. If this is true, then all the terms before the "quadratic" term are small but the quadratic term is extremely small. For example, what if $\Delta x$, $\Delta \theta$, and $\Delta h$ are on the order of $10^{-3}$. This means $\Delta x \Delta \theta$ is on the order of $10^{-6}$ and would thus not contribute all that much to $\Delta y$.
