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 ?

• A. f is continuous at (0, 0)
• B. The partial derivative of f with respect to x is not continuous at (0, 0)
• C. The partial derivative of f with respect to y is continuous at (0, 0)
• D. f is not differentiable at (0, 0)

Answer 1

Answer: (D)

f is not differentiable at (0, 0)

Answer 2

The correct option is (D) : f is not differentiable at (0, 0).