Question:
Let π:βΓβββ be a function defined by
\(f(x,y)=\begin{cases} \frac{xy(x+y}{x^2+y^2} & \quad \text{if }(x,y)β (0,0),\\ 0, & \quad if\,(x,y)=(0,0). \end{cases}\)
Then, which of the following statements is/are TRUE?
Let π:βΓβββ be a function defined by
\(f(x,y)=\begin{cases} \frac{xy(x+y}{x^2+y^2} & \quad \text{if }(x,y)β (0,0),\\ 0, & \quad if\,(x,y)=(0,0). \end{cases}\)
Then, which of the following statements is/are TRUE?
\(f(x,y)=\begin{cases} \frac{xy(x+y}{x^2+y^2} & \quad \text{if }(x,y)β (0,0),\\ 0, & \quad if\,(x,y)=(0,0). \end{cases}\)
Then, which of the following statements is/are TRUE?
Updated On: Oct 1, 2024
- π is continuous on β Γ β
- The partial derivative of π with respect to π¦ exists at (0, 0), and is 0
- The partial derivative of π with respect to π₯ is continuous on β Γ β
- π is NOT differentiable at (0, 0)
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The Correct Option is A, B, D
Solution and Explanation
The correct options are: A, B and D
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