  We develop a hybrid numerical approach to extract the exact memory function
K(t) of a tagged particle in three-dimensional glass-forming liquids. We
compare the behavior of the exact memory kernel to two mean-field approaches,
namely the standard mode-coupling theory and a recently proposed ansatz for the
memory function that forms the basis of a new derivation of the exact form of
K(t) for a fluid with short-ranged interactions in infinite dimensions. Each of
the mean-field functions qualitatively and quantitatively share traits with the
exact K(t), although several important quantitative differences are manifest.
