Ankur posted an Question
January 22, 2021 • 08:52 am 30 points
  • IIT JAM
  • Mathematics (MA)

Consider the function x+y o(x, y) ={ x-y 0 when x# y then otherwise (a) o is discontinuous and both partial derivatives exists at (0, 0) (b) (c) o continuous an

Consider the function x+y o(x, y) ={ x-y 0 when x# y then otherwise (A) o is discontinuous and both partial derivatives exists at (0, 0) (B) (C) o continuous and both partial derivatives exists at (0, 0) o discontinuous and both partial derivatives and not exists at (0, 0) (D) o continuous and both partial derivatives does not exists at (0, 0)

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    Sonu saini

    answer A is correct since difference of power is 2

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    as I put x=r cos(t) ,y=r sin(t). I got continuous

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    look it

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    I want to ask that can't we directly see this by putting x= r cos(t) and y= r sin(t)

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    actually if you put y=mx you will get zero ...but it doesn't imply that your function is continuous because you have another path which implies that limit is not zero

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    if you put rcosx or rsinx you will get zero but this result not imply that function is continuous

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    limit continuity of differentiability in function of two variable is hit and trail method ...because no particular method is still not available which gives 100% correct result

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    but in some cases we show this by putting x=r cos(t) and y= rain(t)

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    yes ....in sum case you put y= mx also but i just want to say that there if you have two way from one way option correct and from another way if option incorrect then option will consider incorrect

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    i think you understand what i want to say you

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    still doubt??

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