Question

quick question on differentiablity of a function. ? in thread.

Answer 1

A function z = f(x; y) is said to be dierentiable at (a; b) if f(x; y) can be
expressed in the form
f(x; y) = f(a; b) + fx(a; b)(x a) + fy(a; b)(y b) + E(x; y)
with the relative error E satisfying
\[\lim_{(x,y) \rightarrow (0,0)} \frac{E(x,y)}{\sqrt{(x-a)^2+(y-b)^2}}=0\]

Answer 2

One does the limit have to be equal to zero or can it just exist, im pretty sure it has to be equal to zero as this is stated but want to make sure, and two, does that mean to prove the function is not differentiable at a the point (a,b), i can just prove the limit does not exist?