  Slender-body approximations have been successfully used to explain many
phenomena in low-Reynolds number fluid mechanics. These approximations
typically use a line of singularity solutions to represent the flow. These
singularities can be difficult to implement numerically because they diverge at
their origin. Hence people have regularized these singularities to overcome
this issue. This regularization blurs the force over a small blob therefore
removing the divergent behaviour. However it is unclear how best to regularize
the singularities to minimize errors. In this paper we investigate if a line of
regularized Stokeslets can describe the flow around a slender body. This is
achieved by comparing the asymptotic behaviour of the flow from the line of
regularized Stokeslets with the results from slender-body theory. We find that
the flow far from the body can be captured if the regularization parameter is
proportional to the radius of the slender body. This is consistent with what is
assumed in numerical simulations and provides a choice for the proportionality
constant. However more stringent requirements must be placed on the
regularization blob to capture the near field flow outside a slender body. This
inability to replicate the local behaviour indicates that many regularizations
cannot satisfy the non-slip boundary conditions on the bodies surface to
leading order, with one of the most commonly used regularizations showing an
angular dependency of velocity along any cross section. This problem can be
overcome with compactly supported blobs { and we construct one such example
blob which could be effectively used to simulate the flow around a slender body
