Part CCSIR NET December 2024every-line-behaves-and-a-parabola-does-not

Every line behaves and a parabola does not

Consider the function $f : R^{2} \to R$ defined by $f (x, y) = x^{2} y / (x^{4} + y^{2}) + e^{(}$ xy) for (x, y) ≠ (0, 0), and f(x, y) = 1 for (x, y) = (0, 0). Which of the following statements are true?

A.f is differentiable on $R^{2}$ \ {(0, 0)}.✓
B.All the directional derivatives of f exist at (0, 0).✓
C.f is differentiable on $R^{2}$ .
D.f is not continuous at (0, 0).✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Every line behaves and a parabola does not

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