Consider the function f : ℝ2 → ℝ defined by
\(f(x, y)= \begin{cases}(x-y)^2 \cos \frac{1}{x-y} & \text { if } x \neq y \\ 0 & \text { if } x=y.\end{cases}\)
Which of the following statement is true?
1
f is continuous at (0, 0).
2
f is not continuous at (0, 0).
3
The partial derivative fx does not exist at (0, 0).
4
The partial derivative fx is continuous at (0, 0) and fx(0,0) = 1.
5
Question Not Attempted