Given a disk $Z$, an analytic function $f$, and an estimate for the range $f(Z)$ in the form of a disk $\{c;R\}$, the following question arises: does $\{c;R\}$ completely contain the complex-valued range $f(Z)$? In this paper we present an approach to checking the above enclosure by using of the method of curvature, which can be suitably applied in some cases. This method is based on Blaschke's result concerning the intersection of a given simple closed smooth boundary of a circle. The method is used for determining the best including approximations for the ranges $\log Z$ and $Z^{1/k}$.