Question:
Let f : \(\R^2 → \R\) be the function defined by
\(f(x,y) = \begin{cases} x^2\sin\frac{1}{x}+y^2\cos y, & x \ne 0 \\ 0, & x=0. \end{cases}\)
Then which one of the following statements is NOT true ?
Let f : \(\R^2 → \R\) be the function defined by
\(f(x,y) = \begin{cases} x^2\sin\frac{1}{x}+y^2\cos y, & x \ne 0 \\ 0, & x=0. \end{cases}\)
Then which one of the following statements is NOT true ?
\(f(x,y) = \begin{cases} x^2\sin\frac{1}{x}+y^2\cos y, & x \ne 0 \\ 0, & x=0. \end{cases}\)
Then which one of the following statements is NOT true ?
Updated On: Oct 1, 2024
- f is continuous at (0, 0)
- The partial derivative of f with respect to x is not continuous at (0, 0)
- The partial derivative of f with respect to y is continuous at (0, 0)
- f is not differentiable at (0, 0)
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The Correct Option is D
Solution and Explanation
The correct option is (D) : f is not differentiable at (0, 0).
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