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###### 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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see this

see this

now I got

• ##### Satpal singh

see the attachment

• ##### Satpal singh

see the attachment

• ##### Sonu saini Best Answer

see the attachment

• ##### Sonu saini

answer A is correct since difference of power is 2

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

look it

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

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

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

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

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

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

i think you understand what i want to say you

still doubt??

• ##### Satpal singh

option a is correct

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