Question

Consider the function \(f(x, y)=\frac{x y}{x^{2}+y^{2}}\) if \((x, y) \neq(0,0)\)

$$ =0 \text { if }(x, y)=(0,0) $$

Which one of the statement is incorrect.

Select one:

a. \(f(x, y)\) is differentiable everywhere.

b. \(f(x, y)\) is differentiable everywhere except at the origin.

c. \(f(x, y)\) is not continuous

d. First partial derivatives \(f(x, y)\) exist.

e. \(\lim _{(x, y) \rightarrow(0,0)} \frac{x y}{x^{2}+y^{2}}\) does not exist.

Answer 1