Question:
Let $f ∶ R^2 → R$ be a function defined as
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?
Let $f ∶ R^2 → R$ be a function defined as
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?
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151
Updated On: Oct 1, 2024
- $ \lim_{(x,y) \rightarrow (0,0)} 𝑓(x, y) = 0$
- $f_x(0, 0) = 0$
- 𝑓(x, y) is not continuous at (0, 0)
- Both $f_x$ and $f_y$ do not exist at (0, 0)
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The Correct Option is B, C
Solution and Explanation
The correct Options are B and C : $ \lim_{(x,y) \rightarrow (0,0)} 𝑓(x, y) = 0$ AND 𝑓(x, y) is not continuous at (0, 0)
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