Mathematics · Real Analysis
Consider the function f : &doublebar;R2 → &doublebar;R defined by: f(x,y) = x2yx4 + y2 + e2y, for (x, y) ≠ (0, 0) f(0,0) = 1 Which of the following statements is TRUE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is continuous at (0, 0) but not differentiable
- 2f is not continuous at (0, 0)✓
- 3All directional derivatives of f exist at (0, 0)
- 4f is differentiable at (0, 0)
Correct answer
f is not continuous at (0, 0)
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