Mixing
Euler's Theorem(Converse deduction)
$begingroup$
In my textbook, it says that: Let f(x,y) be a real valued function such that the two second order partial derivatives are continuous at a point (a,b). Then both of them are equal at (a,b).
I read the proof and got a thought about whether the converse is true or not.
That is if Both of the second order partial derivatives exist and are equal, then whether they are continuous or not. I don't know how to prove this logically. Is the converse true or not? If yes, then please help me with the proof.
calculus
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
$endgroup$
add a comment |
$begingroup$
In my textbook, it says that: Let f(x,y) be a real valued function such that the two second order partial derivatives are continuous at a point (a,b). Then both of them are equal at (a,b).
I read the proof and got a thought about whether the converse is true or not.
That is if Both of the second order partial derivatives exist and are equal, then whether they are continuous or not. I don't know how to prove this logically. Is the converse true or not? If yes, then please help me with the proof.
calculus
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
$endgroup$
add a comment |
$begingroup$
In my textbook, it says that: Let f(x,y) be a real valued function such that the two second order partial derivatives are continuous at a point (a,b). Then both of them are equal at (a,b).
I read the proof and got a thought about whether the converse is true or not.
That is if Both of the second order partial derivatives exist and are equal, then whether they are continuous or not. I don't know how to prove this logically. Is the converse true or not? If yes, then please help me with the proof.
calculus
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
$endgroup$
In my textbook, it says that: Let f(x,y) be a real valued function such that the two second order partial derivatives are continuous at a point (a,b). Then both of them are equal at (a,b).
I read the proof and got a thought about whether the converse is true or not.
That is if Both of the second order partial derivatives exist and are equal, then whether they are continuous or not. I don't know how to prove this logically. Is the converse true or not? If yes, then please help me with the proof.
calculus
calculus
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
asked Jan 26 at 14:50
Shashank DwivediShashank Dwivedi
675
675
add a comment |
add a comment |
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