= Solution
It is useful to rewrite the local <lensing convergence> as
$$
\kappa(\theta)=\theta_E\frac{\theta_c^2+\theta^2/2}{(\theta^2+\theta_c^2)^{3/2}}.
$$
For positive core radius, the requested limits are
$$
\boxed{\kappa(\theta)\sim\frac{\theta_E}{2|\theta|}\longrightarrow0
\quad(|\theta|\to\infty),\qquad
\kappa(0)=\frac{\theta_E}{\theta_c}<\infty.}
$$
A <singular isothermal sphere lens> instead has $\kappa(\theta)=\theta_E/(2|\theta|)$, which diverges at the centre. The finite core of the <softened isothermal lensing potential> regularizes this central <lensing convergence>; at large angular radius the two models have the same leading profile.
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