Eletric potential created by a homogenously charged disc

[victorcell]

Homework Statement

I've to demonstrate the electric potential that a charge q feels when it's broght from infinite to a point z. The problem is that every demonstration i found out there starts with the definition of potential eletric as dV = k. dq/ r²; but i cannot use that, 'cause my professor wants us to go with delta V = - integral ( E. dl). no problem to find the eletric field though. The issue regard the integral

Homework Equations

After the integration, when dealing with the limits, infinite and z, the result comes down to + and - infinite, which is clearly an indertermination mathematicaly speaking, in spite of that, if I'm allowed to cancel that out, the result is just perfect. I am posting the picture of what I've done, I've canceled the infinites justifying by the definition of electric potential been zero at r=infinite; but i am not sure that this is allowed.. thanks for the help

 

[TSny]

Hello, victorcell. Welcome to PF!

To handle the limit of the integral at z = ∞, you need to evaluate $$ \lim_{z \to \infty} (\sqrt{z^2+R^2} - z)$$