Here we show some examples on separating "nice" parts from "tough" parts,
represented by a formula
Note that in the first two examples we eventually dropped the first limit and
left just the second to evaluate, while in the third example we kept the
zero. Here a beginner may be even excused for not evaluating the second limit
at all and proclaim that the whole problem has answer 0. However, we know
that the theorem on limits and operations can be used only if the outcome of
the operations makes sense; that is, if we do not get an indeterminate
expression. In the first two examples, no matter what the second limit is, we
can always get an answer to the whole problem using limit algebra, since
there is no indeterminate expression of the form