I was wondering if there were a mathematical way to note that a variable in an expression is "very small". I feel like ambiguity might be the cause of there not being one, but I'm not sure.
$\Delta A = \frac12 (r + \Delta r)^2 \Delta \theta - \frac12 r^2 \theta = r (\Delta r \Delta \theta) + \frac12(\Delta r)^2 \Delta \theta \approx r \Delta r \Delta \theta$
Error in $\Delta A $ is the term $\frac12 (\Delta r)^2 \Delta \theta$ when $\Delta r$ and $\Delta \theta$ are very small.
Is there a better way to write the bolded statement?
And on that note, is there a better way to write "Error in $\Delta A$"?