  We comment on recent results in the field of information based complexity,
which state (in a number of different settings), that approximation of
infinitely differentiable functions is intractable and suffers from the curse
of dimensionality. We show that renorming the space of infinitely
differentiable functions in a suitable way allows weakly tractable uniform
approximation by using only function values. Moreover, the approximating
algorithm is based on a simple application of Taylor's expansion at the center
of the unit cube. We discuss also the approximation on the Euclidean ball and
the approximation in the $L_1$-norm, which is closely related to the problem of
numerical integration.
