# plot and limit are not in agreement

I am plotting the following function $$\frac{\sqrt{t \text{ \omega_c }}-\sqrt{\pi } e^{\frac{1}{t \text{ \omega_c }}} \text{erfc}\left(\frac{1}{\sqrt{t \text{ \omega_c }}}\right)}{(t \text{ \omega_c })^{3/2}}$$ for $$\omega_c=1$$

 (Sqrt[t*\[Omega]c] - E^(1/(t*\[Omega]c))*Sqrt[Pi]*Erfc[1/Sqrt[t*\[Omega]c]])/(t*\[Omega]c)^(3/2) 

and I am obtaining

where we clearly see that the function diverges as $$t \rightarrow 0$$. What is interesting is that if I perform the limit through Mathematica for $$t\rightarrow 0$$ I obtain

which clearly disagrees with the graph. It is important to note that for $$t\approx 10^{-3}$$ the graph tends to the same correct limit, indicated by the blue line. Is there any way to increase the precision of the plot?