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Exam 2024-01-13 Question 5

Exam 2024-01-13 Question 5

by Sofie Angere -
Number of replies: 3

Hello, I have a question about question 5. Perhaps it's just something I've missed so far, but doesn't the implicit function theorem require that the equations defining the hypersurface are zero on the point we apply it to? As far as I can see, neither the function xu + y^2v nor the function xv^4-y^3u^5 are zero at (x=1, y=-1, u=0, v=1)? Or are the equations given meant to be transformed somehow?


Thanks,

Sofie

In reply to Sofie Angere

Sv: Exam 2024-01-13 Question 5

by Anna Nauclér -
Hi,

I am wondering the same thing! Have you found an answer or explanation yet?

Thanks,
Anna
In reply to Anna Nauclér

Re: Sv: Exam 2024-01-13 Question 5

by Sofie Angere -
Hi Anna,

no, unfortunately not. It's possible to just solve for u and v though, and then differentiate the functions you get from that. I'm not at all sure that's what we're supposed to do, though.

Sofie
In reply to Sofie Angere

Sv: Exam 2024-01-13 Question 5

by Kilian Liebe -
Hi!

I think the most likely answer is that it was meant to be the point (1,-1,0,0) in the question, or that the equations should be =1 instead, and then the theorem becomes applicable, but I'm not completely sure. I will think about it a bit more and then get back to you.