Question:

Let 𝑓: R2 β†’ R be the function defined by
𝑓(π‘₯, 𝑦) = { π‘₯2 βˆ’ 𝑦3π‘₯2+𝑦2,(π‘₯, 𝑦) β‰  (0, 0) 0 , (π‘₯, 𝑦) = (0, 0)
Then

Updated On: Oct 1, 2024
  • 𝑓 is not continuous at (0, 0)
  • 𝑓π‘₯ (0, 0) = 0
  • 𝑓𝑦 (0, 0) = βˆ’1
  • 𝑓π‘₯ (0, 0) does not exists
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The Correct Option is A, C, D

Solution and Explanation

The correct options is (A): 𝑓 is not continuous at (0, 0), (C): 𝑓𝑦 (0, 0) = βˆ’1 and (D): 𝑓π‘₯ (0, 0) does not exists
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