Taylor polynomial of third degree and error estimation

It seems that I'm a little bit lost about this exercise. It says: Find the taylors polynomial of third degree centered at the origin for . Estimate the error for: .

So, I did the first part (the easy one), the taylors polynomial for z at (0,0) looks like this:

Then I've found the expression for the error:

Now, how do I estimate the error? I have to say that the error will be something like , I have to find "k". Should I consider ? How do I proceed from there?

Bye and thanks for posting!