  We discuss preliminary results for the vector form factors $f_+^{\{\pi,K\}}$
at zero-momentum transfer for the decays $D\to\pi\ell\nu$ and $D\to K \ell\nu$
using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx
0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the
(degenerate) physical light quark mass. We use the kinematic constraint
$f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from our
study of the scalar current, which yields $f_0(0)$. Results are extrapolated to
the continuum physical point in the framework of hard pion/kaon SU(3)
heavy-meson-staggered $\chi$PT and Symanzik effective theory. Our calculation
improves upon the precision achieved in existing lattice-QCD calculations of
the vector form factors at $q^2=0$. We show the values of the CKM matrix
elements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminary
results for the form factors together with recent experimental results, and
discuss the implications of these values for the second row CKM unitarity.
