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Working my way through Spivak "Calculus on Manifolds."
On p. 34, problem 2-33, the problem asks "show that the continuity of D1f[tex]^{i}[/tex] at a can be eliminated from the hypothesis of Theorem 2-8.
Is this a typo? Is he saying that there is no need for continuity of ONE partial derivative, or no need for continuity of ANY of the partial derivatives?
If the latter, please don't give me the answer yet; I'll struggle with it some more.
I've been assuming this is a typo, and should be Di and not D1; haven't been able to do it yet though.
Thank you!
Ken Cohen
On p. 34, problem 2-33, the problem asks "show that the continuity of D1f[tex]^{i}[/tex] at a can be eliminated from the hypothesis of Theorem 2-8.
Is this a typo? Is he saying that there is no need for continuity of ONE partial derivative, or no need for continuity of ANY of the partial derivatives?
If the latter, please don't give me the answer yet; I'll struggle with it some more.
I've been assuming this is a typo, and should be Di and not D1; haven't been able to do it yet though.
Thank you!
Ken Cohen