Heat equation steady state boundary condition question

Question

consider the following question and the part of the solution to calculate the radial part:

The solution for the R part

Could someone please clarify why c2 = 0 as i am a bit confused as to why this is.

Answer 1

Boundary condition 3 and not 1 states that $R(r)$ is finite everywhere. So $R(0)$ must also be finite and it's the case only if $c_2=0$ then $R(0)=0$ and is defined. If $c_2 \neq 0$ then: $$R(0)=c_1r^l+c_2r^{-l-1}=c_1\times 0 + \frac {c_2} 0$$