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Mathematics for Economy Question on Preliminaries and functions

Let š‘“: R2 ā†’ R be the function defined by
š‘“š‘„, š‘¦ = { š‘„2 āˆ’ š‘¦3š‘„2+š‘¦2,š‘„, š‘¦ ā‰  0, 0 0 , š‘„, š‘¦ = 0, 0
Then

A

š‘“ is not continuous at (0, 0)

B

š‘“š‘„ (0, 0) = 0

C

š‘“š‘¦ (0, 0) = āˆ’1

D

š‘“š‘„ (0, 0) does not exists

Answer

š‘“ is not continuous at (0, 0)

Explanation

Solution

The correct options is (A): š‘“ is not continuous at (0, 0), (C): š‘“š‘¦ (0, 0) = āˆ’1 and (D): š‘“š‘„ (0, 0) does not exists