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

Answer: (D)

f(x,y) is not continuous at origin

Answer 2

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