Question

If f: R²→R² is a function defined as \(f(x,y) =   \begin{cases}   \frac{x}{\sqrt{x^2+y^2}},      & x\neq0,y\neq0\\     2,  & x=0,y=0   \end{cases}\)then, which of the following is correct?

• A. f(x,y) is continuous at origin
• B. f(x,y) is differentiable at origin
• C. \(\lim\limits_{(x,y)\rightarrow(0,0)}\) f(x,y) exists and is equal to 2
• D. f(x,y) is not continuous at origin

Answer 1

The Correct Option is D

The correct answer is(D): f(x,y) is not continuous at origin