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?
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?
Updated On: Mar 12, 2025
- f(x,y) is continuous at origin
- f(x,y) is differentiable at origin
- \(\lim\limits_{(x,y)\rightarrow(0,0)}\) f(x,y) exists and is equal to 2
- f(x,y) is not continuous at origin
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The Correct Option is D
Solution and Explanation
The correct answer is(D): f(x,y) is not continuous at origin
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