  We give a complete classification of bicovariant first order differential
calculi on the quantum enveloping algebra U_q(b+) which we view as the quantum
function algebra C_q(B+). Here, b+ is the Borel subalgebra of sl_2. We do the
same in the classical limit q->1 and obtain a one-to-one correspondence in the
finite dimensional case. It turns out that the classification is essentially
given by finite subsets of the positive integers. We proceed to investigate the
classical limit from the dual point of view, i.e. with ``function algebra''
U(b+) and ``enveloping algebra'' C(B+). In this case there are many more
differential calculi than coming from the q-deformed setting. As an
application, we give the natural intrinsic 4-dimensional calculus of
kappa-Minkowski space and the associated formal integral.
