  Inspired by the works of Dewar, Murty and Kot\v{e}\v{s}ovec, we establish
some useful theorems for asymptotic formulas. As an application, we obtain
asymptotic formulas for the numbers of skew plane partitions and cylindric
partitions. We prove that the order of the asymptotic formula for the skew
plane partitions of fixed width depends only on the width of the region, not on
the profile (the skew zone) itself, while this is not true for cylindric
partitions.
