tells you that the distance between x and x_0 is less than epsilon (i.e. ).
tells you that .
Do you see why you get continuity by picking delta as you did?
g(x, y) = x
I am trying to prove that g is continuous on using the epsilon-delta definition of continuity.
I gave it a try but it doesn't look right:
Given and , set
Then whenever , it follows that
Thanks for any help in advance.