I need help with a continuity problem on functions of several variables

[cyrano]

Hello everyone , I am new here so sorry if I misuse the forum. I need help with the above problem. I intiutively understand but do not know how to show, how to start the proof. I would be glad if anyone helps.

 

[lev888]

I'm guessing the definition of a continuous function would be helpful.

 

[Deleted member 4993]

Assume:

p_o is at (x_o,y_o)

and apply definition (condition) of continuity.....